Opened 11 years ago
Closed 11 years ago
#3521 closed defect (fixed)
[with patch; with positive review] Atkin-Lehner operator doesn't square to 1
Reported by: | roed | Owned by: | craigcitro |
---|---|---|---|
Priority: | major | Milestone: | sage-3.0.4 |
Component: | modular forms | Keywords: | modular symbols, atkin-lehner |
Cc: | Merged in: | ||
Authors: | Reviewers: | ||
Report Upstream: | Work issues: | ||
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description
The following should produce the identity matrix:
sage: e = (DirichletGroup(13).0)^2 sage: M = ModularSymbols(e, 2) sage: M.atkin_lehner_operator().matrix()^2 [ 1 0 0 0] [ 0 1 0 0] [-zeta6 - 1 0 1 zeta6 + 1] [ zeta6 + 1 0 0 -zeta6]
Attachments (2)
Change History (6)
comment:1 Changed 11 years ago by
Changed 11 years ago by
comment:2 Changed 11 years ago by
- Summary changed from Atkin-Lehner operator doesn't square to 1 to [with patch; needs review] Atkin-Lehner operator doesn't square to 1
WARNING:
The atkin-lehner operator does *not* leave the space $M_k(N,\chi)$ invariant unless $\chi$ is quadratic. Really it sends $M_k(N,\chi)$ to $M_k(N,\chibar)$. So Sage should give an error message when $\chi$ is not quadratic.
Changed 11 years ago by
comment:3 Changed 11 years ago by
- Summary changed from [with patch; needs review] Atkin-Lehner operator doesn't square to 1 to [with patch; with positive review] Atkin-Lehner operator doesn't square to 1
Looks good. I added a patch that actually corrects a bug (some statements were out of order), and just reformats/corrects typos. This is ready to go.
comment:4 Changed 11 years ago by
- Milestone changed from sage-3.1.1 to sage-3.0.4
- Resolution set to fixed
- Status changed from new to closed
Merged in Sage 3.0.4.alpha2
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For me this illustrates the bug more clearly: