Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(365))\).
|
Total |
New |
Old |
Modular forms
| 5616 |
5095 |
521 |
Cusp forms
| 5041 |
4667 |
374 |
Eisenstein series
| 575 |
428 |
147 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(365))\)
We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.
Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
365.2.a |
\(\chi_{365}(1, \cdot)\) |
365.2.a.a |
2 |
1 |
365.2.a.b |
3 |
365.2.a.c |
5 |
365.2.a.d |
7 |
365.2.a.e |
8 |
365.2.b |
\(\chi_{365}(74, \cdot)\) |
365.2.b.a |
36 |
1 |
365.2.c |
\(\chi_{365}(364, \cdot)\) |
365.2.c.a |
36 |
1 |
365.2.d |
\(\chi_{365}(291, \cdot)\) |
365.2.d.a |
26 |
1 |
365.2.e |
\(\chi_{365}(81, \cdot)\) |
365.2.e.a |
26 |
2 |
365.2.e.b |
26 |
365.2.f |
\(\chi_{365}(119, \cdot)\) |
365.2.f.a |
68 |
2 |
365.2.k |
\(\chi_{365}(46, \cdot)\) |
365.2.k.a |
52 |
2 |
365.2.l |
\(\chi_{365}(211, \cdot)\) |
365.2.l.a |
4 |
2 |
365.2.l.b |
48 |
365.2.m |
\(\chi_{365}(64, \cdot)\) |
365.2.m.a |
72 |
2 |
365.2.n |
\(\chi_{365}(9, \cdot)\) |
365.2.n.a |
72 |
2 |
365.2.p |
\(\chi_{365}(168, \cdot)\) |
365.2.p.a |
140 |
4 |
365.2.q |
\(\chi_{365}(22, \cdot)\) |
365.2.q.a |
140 |
4 |
365.2.s |
\(\chi_{365}(16, \cdot)\) |
365.2.s.a |
72 |
6 |
365.2.s.b |
72 |
365.2.t |
\(\chi_{365}(76, \cdot)\) |
365.2.t.a |
104 |
4 |
365.2.y |
\(\chi_{365}(24, \cdot)\) |
365.2.y.a |
136 |
4 |
365.2.z |
\(\chi_{365}(36, \cdot)\) |
365.2.z.a |
144 |
6 |
365.2.ba |
\(\chi_{365}(69, \cdot)\) |
365.2.ba.a |
216 |
6 |
365.2.bb |
\(\chi_{365}(4, \cdot)\) |
365.2.bb.a |
216 |
6 |
365.2.bd |
\(\chi_{365}(7, \cdot)\) |
365.2.bd.a |
280 |
8 |
365.2.be |
\(\chi_{365}(52, \cdot)\) |
365.2.be.a |
280 |
8 |
365.2.bg |
\(\chi_{365}(19, \cdot)\) |
365.2.bg.a |
408 |
12 |
365.2.bl |
\(\chi_{365}(6, \cdot)\) |
365.2.bl.a |
288 |
12 |
365.2.bm |
\(\chi_{365}(28, \cdot)\) |
365.2.bm.a |
840 |
24 |
365.2.bp |
\(\chi_{365}(13, \cdot)\) |
365.2.bp.a |
840 |
24 |