Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(912))\).
|
Total |
New |
Old |
Modular forms
| 24048 |
9820 |
14228 |
Cusp forms
| 22033 |
9512 |
12521 |
Eisenstein series
| 2015 |
308 |
1707 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(912))\)
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 the newforms together with their dimension.
Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
912.2.a |
\(\chi_{912}(1, \cdot)\) |
912.2.a.a |
1 |
1 |
912.2.a.b |
1 |
912.2.a.c |
1 |
912.2.a.d |
1 |
912.2.a.e |
1 |
912.2.a.f |
1 |
912.2.a.g |
1 |
912.2.a.h |
1 |
912.2.a.i |
1 |
912.2.a.j |
1 |
912.2.a.k |
1 |
912.2.a.l |
1 |
912.2.a.m |
2 |
912.2.a.n |
2 |
912.2.a.o |
2 |
912.2.d |
\(\chi_{912}(191, \cdot)\) |
912.2.d.a |
12 |
1 |
912.2.d.b |
24 |
912.2.e |
\(\chi_{912}(151, \cdot)\) |
None |
0 |
1 |
912.2.f |
\(\chi_{912}(113, \cdot)\) |
912.2.f.a |
2 |
1 |
912.2.f.b |
2 |
912.2.f.c |
2 |
912.2.f.d |
2 |
912.2.f.e |
2 |
912.2.f.f |
4 |
912.2.f.g |
4 |
912.2.f.h |
10 |
912.2.f.i |
10 |
912.2.g |
\(\chi_{912}(457, \cdot)\) |
None |
0 |
1 |
912.2.j |
\(\chi_{912}(647, \cdot)\) |
None |
0 |
1 |
912.2.k |
\(\chi_{912}(607, \cdot)\) |
912.2.k.a |
2 |
1 |
912.2.k.b |
2 |
912.2.k.c |
2 |
912.2.k.d |
2 |
912.2.k.e |
2 |
912.2.k.f |
2 |
912.2.k.g |
4 |
912.2.k.h |
4 |
912.2.p |
\(\chi_{912}(569, \cdot)\) |
None |
0 |
1 |
912.2.q |
\(\chi_{912}(49, \cdot)\) |
912.2.q.a |
2 |
2 |
912.2.q.b |
2 |
912.2.q.c |
2 |
912.2.q.d |
2 |
912.2.q.e |
2 |
912.2.q.f |
2 |
912.2.q.g |
4 |
912.2.q.h |
4 |
912.2.q.i |
4 |
912.2.q.j |
4 |
912.2.q.k |
6 |
912.2.q.l |
6 |
912.2.r |
\(\chi_{912}(341, \cdot)\) |
912.2.r.a |
312 |
2 |
912.2.u |
\(\chi_{912}(229, \cdot)\) |
912.2.u.a |
72 |
2 |
912.2.u.b |
72 |
912.2.v |
\(\chi_{912}(419, \cdot)\) |
912.2.v.a |
288 |
2 |
912.2.y |
\(\chi_{912}(379, \cdot)\) |
912.2.y.a |
160 |
2 |
912.2.bb |
\(\chi_{912}(31, \cdot)\) |
912.2.bb.a |
2 |
2 |
912.2.bb.b |
2 |
912.2.bb.c |
4 |
912.2.bb.d |
4 |
912.2.bb.e |
6 |
912.2.bb.f |
6 |
912.2.bb.g |
8 |
912.2.bb.h |
8 |
912.2.bc |
\(\chi_{912}(311, \cdot)\) |
None |
0 |
2 |
912.2.bd |
\(\chi_{912}(521, \cdot)\) |
None |
0 |
2 |
912.2.bg |
\(\chi_{912}(103, \cdot)\) |
None |
0 |
2 |
912.2.bh |
\(\chi_{912}(239, \cdot)\) |
912.2.bh.a |
2 |
2 |
912.2.bh.b |
2 |
912.2.bh.c |
2 |
912.2.bh.d |
2 |
912.2.bh.e |
24 |
912.2.bh.f |
24 |
912.2.bh.g |
24 |
912.2.bm |
\(\chi_{912}(121, \cdot)\) |
None |
0 |
2 |
912.2.bn |
\(\chi_{912}(65, \cdot)\) |
912.2.bn.a |
2 |
2 |
912.2.bn.b |
2 |
912.2.bn.c |
2 |
912.2.bn.d |
2 |
912.2.bn.e |
2 |
912.2.bn.f |
2 |
912.2.bn.g |
4 |
912.2.bn.h |
4 |
912.2.bn.i |
4 |
912.2.bn.j |
4 |
912.2.bn.k |
4 |
912.2.bn.l |
4 |
912.2.bn.m |
8 |
912.2.bn.n |
16 |
912.2.bn.o |
16 |
912.2.bo |
\(\chi_{912}(289, \cdot)\) |
912.2.bo.a |
6 |
6 |
912.2.bo.b |
6 |
912.2.bo.c |
6 |
912.2.bo.d |
6 |
912.2.bo.e |
6 |
912.2.bo.f |
6 |
912.2.bo.g |
12 |
912.2.bo.h |
12 |
912.2.bo.i |
12 |
912.2.bo.j |
12 |
912.2.bo.k |
18 |
912.2.bo.l |
18 |
912.2.bq |
\(\chi_{912}(277, \cdot)\) |
912.2.bq.a |
320 |
4 |
912.2.br |
\(\chi_{912}(221, \cdot)\) |
912.2.br.a |
624 |
4 |
912.2.bu |
\(\chi_{912}(259, \cdot)\) |
912.2.bu.a |
320 |
4 |
912.2.bv |
\(\chi_{912}(11, \cdot)\) |
912.2.bv.a |
8 |
4 |
912.2.bv.b |
8 |
912.2.bv.c |
608 |
912.2.bz |
\(\chi_{912}(41, \cdot)\) |
None |
0 |
6 |
912.2.ca |
\(\chi_{912}(25, \cdot)\) |
None |
0 |
6 |
912.2.cc |
\(\chi_{912}(257, \cdot)\) |
912.2.cc.a |
6 |
6 |
912.2.cc.b |
6 |
912.2.cc.c |
18 |
912.2.cc.d |
18 |
912.2.cc.e |
24 |
912.2.cc.f |
36 |
912.2.cc.g |
60 |
912.2.cc.h |
60 |
912.2.cf |
\(\chi_{912}(295, \cdot)\) |
None |
0 |
6 |
912.2.ch |
\(\chi_{912}(47, \cdot)\) |
912.2.ch.a |
6 |
6 |
912.2.ch.b |
6 |
912.2.ch.c |
6 |
912.2.ch.d |
6 |
912.2.ch.e |
72 |
912.2.ch.f |
72 |
912.2.ch.g |
72 |
912.2.ci |
\(\chi_{912}(79, \cdot)\) |
912.2.ci.a |
6 |
6 |
912.2.ci.b |
6 |
912.2.ci.c |
12 |
912.2.ci.d |
12 |
912.2.ci.e |
18 |
912.2.ci.f |
18 |
912.2.ci.g |
24 |
912.2.ci.h |
24 |
912.2.ck |
\(\chi_{912}(23, \cdot)\) |
None |
0 |
6 |
912.2.cn |
\(\chi_{912}(67, \cdot)\) |
912.2.cn.a |
960 |
12 |
912.2.cp |
\(\chi_{912}(35, \cdot)\) |
912.2.cp.a |
1872 |
12 |
912.2.cq |
\(\chi_{912}(61, \cdot)\) |
912.2.cq.a |
960 |
12 |
912.2.cs |
\(\chi_{912}(29, \cdot)\) |
912.2.cs.a |
1872 |
12 |