Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3751))\).
|
Total |
New |
Old |
Modular forms
| 5061 |
4305 |
756 |
Cusp forms
| 261 |
230 |
31 |
Eisenstein series
| 4800 |
4075 |
725 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3751))\)
We only show spaces with odd 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 |
3751.1.c |
\(\chi_{3751}(2419, \cdot)\) |
None |
0 |
1 |
3751.1.d |
\(\chi_{3751}(1332, \cdot)\) |
3751.1.d.a |
1 |
1 |
3751.1.d.b |
1 |
3751.1.d.c |
2 |
3751.1.d.d |
3 |
3751.1.d.e |
3 |
3751.1.d.f |
6 |
3751.1.l |
\(\chi_{3751}(1451, \cdot)\) |
3751.1.l.a |
4 |
2 |
3751.1.n |
\(\chi_{3751}(243, \cdot)\) |
3751.1.n.a |
2 |
2 |
3751.1.o |
\(\chi_{3751}(717, \cdot)\) |
3751.1.o.a |
4 |
4 |
3751.1.q |
\(\chi_{3751}(1170, \cdot)\) |
3751.1.q.a |
4 |
4 |
3751.1.r |
\(\chi_{3751}(27, \cdot)\) |
3751.1.r.a |
4 |
4 |
3751.1.s |
\(\chi_{3751}(511, \cdot)\) |
3751.1.s.a |
4 |
4 |
3751.1.t |
\(\chi_{3751}(2138, \cdot)\) |
3751.1.t.a |
4 |
4 |
3751.1.t.b |
4 |
3751.1.t.c |
4 |
3751.1.t.d |
8 |
3751.1.t.e |
12 |
3751.1.t.f |
12 |
3751.1.t.g |
24 |
3751.1.u |
\(\chi_{3751}(122, \cdot)\) |
3751.1.u.a |
4 |
4 |
3751.1.w |
\(\chi_{3751}(94, \cdot)\) |
None |
0 |
4 |
3751.1.x |
\(\chi_{3751}(481, \cdot)\) |
3751.1.x.a |
4 |
4 |
3751.1.y |
\(\chi_{3751}(1492, \cdot)\) |
3751.1.y.a |
4 |
4 |
3751.1.z |
\(\chi_{3751}(1814, \cdot)\) |
None |
0 |
4 |
3751.1.be |
\(\chi_{3751}(233, \cdot)\) |
3751.1.be.a |
4 |
4 |
3751.1.bf |
\(\chi_{3751}(1455, \cdot)\) |
3751.1.bf.a |
4 |
4 |
3751.1.bn |
\(\chi_{3751}(309, \cdot)\) |
None |
0 |
10 |
3751.1.bp |
\(\chi_{3751}(32, \cdot)\) |
None |
0 |
10 |
3751.1.br |
\(\chi_{3751}(360, \cdot)\) |
3751.1.br.a |
8 |
8 |
3751.1.bs |
\(\chi_{3751}(606, \cdot)\) |
3751.1.bs.a |
8 |
8 |
3751.1.bt |
\(\chi_{3751}(130, \cdot)\) |
3751.1.bt.a |
8 |
8 |
3751.1.bu |
\(\chi_{3751}(487, \cdot)\) |
3751.1.bu.a |
8 |
8 |
3751.1.bv |
\(\chi_{3751}(3, \cdot)\) |
3751.1.bv.a |
8 |
8 |
3751.1.bw |
\(\chi_{3751}(251, \cdot)\) |
3751.1.bw.a |
8 |
8 |
3751.1.bx |
\(\chi_{3751}(40, \cdot)\) |
3751.1.bx.a |
8 |
8 |
3751.1.cc |
\(\chi_{3751}(483, \cdot)\) |
None |
0 |
8 |
3751.1.cd |
\(\chi_{3751}(112, \cdot)\) |
3751.1.cd.a |
8 |
8 |
3751.1.ce |
\(\chi_{3751}(578, \cdot)\) |
3751.1.ce.a |
8 |
8 |
3751.1.cf |
\(\chi_{3751}(118, \cdot)\) |
3751.1.cf.a |
8 |
8 |
3751.1.cf.b |
16 |
3751.1.ch |
\(\chi_{3751}(323, \cdot)\) |
3751.1.ch.a |
8 |
8 |
3751.1.cp |
\(\chi_{3751}(254, \cdot)\) |
None |
0 |
20 |
3751.1.cq |
\(\chi_{3751}(87, \cdot)\) |
None |
0 |
20 |
3751.1.cs |
\(\chi_{3751}(15, \cdot)\) |
None |
0 |
40 |
3751.1.cu |
\(\chi_{3751}(109, \cdot)\) |
None |
0 |
40 |
3751.1.cv |
\(\chi_{3751}(2, \cdot)\) |
None |
0 |
40 |
3751.1.cw |
\(\chi_{3751}(95, \cdot)\) |
None |
0 |
40 |
3751.1.cx |
\(\chi_{3751}(63, \cdot)\) |
None |
0 |
40 |
3751.1.dc |
\(\chi_{3751}(194, \cdot)\) |
None |
0 |
40 |
3751.1.dd |
\(\chi_{3751}(58, \cdot)\) |
None |
0 |
40 |
3751.1.de |
\(\chi_{3751}(23, \cdot)\) |
None |
0 |
40 |
3751.1.df |
\(\chi_{3751}(92, \cdot)\) |
None |
0 |
40 |
3751.1.dg |
\(\chi_{3751}(170, \cdot)\) |
None |
0 |
40 |
3751.1.dh |
\(\chi_{3751}(201, \cdot)\) |
None |
0 |
40 |
3751.1.di |
\(\chi_{3751}(35, \cdot)\) |
None |
0 |
40 |
3751.1.dq |
\(\chi_{3751}(42, \cdot)\) |
None |
0 |
80 |
3751.1.dr |
\(\chi_{3751}(50, \cdot)\) |
None |
0 |
80 |
3751.1.dw |
\(\chi_{3751}(129, \cdot)\) |
None |
0 |
80 |
3751.1.dx |
\(\chi_{3751}(173, \cdot)\) |
None |
0 |
80 |
3751.1.dy |
\(\chi_{3751}(7, \cdot)\) |
None |
0 |
80 |
3751.1.dz |
\(\chi_{3751}(10, \cdot)\) |
None |
0 |
80 |
3751.1.eb |
\(\chi_{3751}(53, \cdot)\) |
None |
0 |
80 |
3751.1.ec |
\(\chi_{3751}(137, \cdot)\) |
None |
0 |
80 |
3751.1.ed |
\(\chi_{3751}(26, \cdot)\) |
None |
0 |
80 |
3751.1.ee |
\(\chi_{3751}(12, \cdot)\) |
None |
0 |
80 |
3751.1.ef |
\(\chi_{3751}(48, \cdot)\) |
None |
0 |
80 |
3751.1.eh |
\(\chi_{3751}(18, \cdot)\) |
None |
0 |
80 |