Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(880))\).
|
Total |
New |
Old |
Modular forms
| 24160 |
11926 |
12234 |
Cusp forms
| 21921 |
11438 |
10483 |
Eisenstein series
| 2239 |
488 |
1751 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(880))\)
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 |
880.2.a |
\(\chi_{880}(1, \cdot)\) |
880.2.a.a |
1 |
1 |
880.2.a.b |
1 |
880.2.a.c |
1 |
880.2.a.d |
1 |
880.2.a.e |
1 |
880.2.a.f |
1 |
880.2.a.g |
1 |
880.2.a.h |
1 |
880.2.a.i |
1 |
880.2.a.j |
1 |
880.2.a.k |
2 |
880.2.a.l |
2 |
880.2.a.m |
2 |
880.2.a.n |
2 |
880.2.a.o |
2 |
880.2.b |
\(\chi_{880}(529, \cdot)\) |
880.2.b.a |
2 |
1 |
880.2.b.b |
2 |
880.2.b.c |
2 |
880.2.b.d |
2 |
880.2.b.e |
2 |
880.2.b.f |
2 |
880.2.b.g |
2 |
880.2.b.h |
4 |
880.2.b.i |
4 |
880.2.b.j |
8 |
880.2.c |
\(\chi_{880}(439, \cdot)\) |
None |
0 |
1 |
880.2.f |
\(\chi_{880}(351, \cdot)\) |
880.2.f.a |
2 |
1 |
880.2.f.b |
2 |
880.2.f.c |
4 |
880.2.f.d |
8 |
880.2.f.e |
8 |
880.2.g |
\(\chi_{880}(441, \cdot)\) |
None |
0 |
1 |
880.2.l |
\(\chi_{880}(89, \cdot)\) |
None |
0 |
1 |
880.2.m |
\(\chi_{880}(879, \cdot)\) |
880.2.m.a |
2 |
1 |
880.2.m.b |
2 |
880.2.m.c |
4 |
880.2.m.d |
4 |
880.2.m.e |
8 |
880.2.m.f |
8 |
880.2.m.g |
8 |
880.2.p |
\(\chi_{880}(791, \cdot)\) |
None |
0 |
1 |
880.2.s |
\(\chi_{880}(67, \cdot)\) |
880.2.s.a |
4 |
2 |
880.2.s.b |
236 |
880.2.t |
\(\chi_{880}(197, \cdot)\) |
880.2.t.a |
8 |
2 |
880.2.t.b |
272 |
880.2.v |
\(\chi_{880}(131, \cdot)\) |
880.2.v.a |
192 |
2 |
880.2.w |
\(\chi_{880}(221, \cdot)\) |
880.2.w.a |
72 |
2 |
880.2.w.b |
88 |
880.2.z |
\(\chi_{880}(23, \cdot)\) |
None |
0 |
2 |
880.2.bb |
\(\chi_{880}(153, \cdot)\) |
None |
0 |
2 |
880.2.bd |
\(\chi_{880}(417, \cdot)\) |
880.2.bd.a |
4 |
2 |
880.2.bd.b |
4 |
880.2.bd.c |
4 |
880.2.bd.d |
4 |
880.2.bd.e |
4 |
880.2.bd.f |
4 |
880.2.bd.g |
4 |
880.2.bd.h |
8 |
880.2.bd.i |
32 |
880.2.bf |
\(\chi_{880}(287, \cdot)\) |
880.2.bf.a |
2 |
2 |
880.2.bf.b |
2 |
880.2.bf.c |
2 |
880.2.bf.d |
2 |
880.2.bf.e |
6 |
880.2.bf.f |
6 |
880.2.bf.g |
20 |
880.2.bf.h |
20 |
880.2.bh |
\(\chi_{880}(309, \cdot)\) |
880.2.bh.a |
240 |
2 |
880.2.bi |
\(\chi_{880}(219, \cdot)\) |
880.2.bi.a |
4 |
2 |
880.2.bi.b |
4 |
880.2.bi.c |
16 |
880.2.bi.d |
256 |
880.2.bk |
\(\chi_{880}(243, \cdot)\) |
880.2.bk.a |
4 |
2 |
880.2.bk.b |
236 |
880.2.bl |
\(\chi_{880}(373, \cdot)\) |
880.2.bl.a |
8 |
2 |
880.2.bl.b |
272 |
880.2.bo |
\(\chi_{880}(81, \cdot)\) |
880.2.bo.a |
4 |
4 |
880.2.bo.b |
4 |
880.2.bo.c |
8 |
880.2.bo.d |
8 |
880.2.bo.e |
8 |
880.2.bo.f |
8 |
880.2.bo.g |
8 |
880.2.bo.h |
8 |
880.2.bo.i |
12 |
880.2.bo.j |
12 |
880.2.bo.k |
16 |
880.2.bp |
\(\chi_{880}(151, \cdot)\) |
None |
0 |
4 |
880.2.bs |
\(\chi_{880}(79, \cdot)\) |
880.2.bs.a |
48 |
4 |
880.2.bs.b |
96 |
880.2.bt |
\(\chi_{880}(9, \cdot)\) |
None |
0 |
4 |
880.2.by |
\(\chi_{880}(201, \cdot)\) |
None |
0 |
4 |
880.2.bz |
\(\chi_{880}(271, \cdot)\) |
880.2.bz.a |
16 |
4 |
880.2.bz.b |
16 |
880.2.bz.c |
32 |
880.2.bz.d |
32 |
880.2.cc |
\(\chi_{880}(39, \cdot)\) |
None |
0 |
4 |
880.2.cd |
\(\chi_{880}(49, \cdot)\) |
880.2.cd.a |
8 |
4 |
880.2.cd.b |
16 |
880.2.cd.c |
16 |
880.2.cd.d |
24 |
880.2.cd.e |
72 |
880.2.cg |
\(\chi_{880}(237, \cdot)\) |
880.2.cg.a |
1120 |
8 |
880.2.ch |
\(\chi_{880}(3, \cdot)\) |
880.2.ch.a |
1120 |
8 |
880.2.ci |
\(\chi_{880}(19, \cdot)\) |
880.2.ci.a |
1120 |
8 |
880.2.cl |
\(\chi_{880}(69, \cdot)\) |
880.2.cl.a |
1120 |
8 |
880.2.cm |
\(\chi_{880}(17, \cdot)\) |
880.2.cm.a |
32 |
8 |
880.2.cm.b |
48 |
880.2.cm.c |
48 |
880.2.cm.d |
144 |
880.2.co |
\(\chi_{880}(47, \cdot)\) |
880.2.co.a |
96 |
8 |
880.2.co.b |
192 |
880.2.cq |
\(\chi_{880}(103, \cdot)\) |
None |
0 |
8 |
880.2.cs |
\(\chi_{880}(57, \cdot)\) |
None |
0 |
8 |
880.2.cu |
\(\chi_{880}(141, \cdot)\) |
880.2.cu.a |
768 |
8 |
880.2.cx |
\(\chi_{880}(51, \cdot)\) |
880.2.cx.a |
768 |
8 |
880.2.cy |
\(\chi_{880}(13, \cdot)\) |
880.2.cy.a |
1120 |
8 |
880.2.cz |
\(\chi_{880}(147, \cdot)\) |
880.2.cz.a |
1120 |
8 |