Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3871))\).
|
Total |
New |
Old |
| Modular forms
| 5023 |
3988 |
1035 |
| Cusp forms
| 343 |
253 |
90 |
| Eisenstein series
| 4680 |
3735 |
945 |
The following table gives the dimensions of subspaces with specified projective image type.
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3871))\)
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 available newforms together with their dimension.
| Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
| 3871.1.b |
\(\chi_{3871}(1028, \cdot)\) |
None |
0 |
1 |
| 3871.1.c |
\(\chi_{3871}(2843, \cdot)\) |
3871.1.c.a |
1 |
1 |
| 3871.1.c.b |
2 |
| 3871.1.c.c |
2 |
| 3871.1.c.d |
4 |
| 3871.1.c.e |
8 |
| 3871.1.i |
\(\chi_{3871}(3057, \cdot)\) |
3871.1.i.a |
2 |
2 |
| 3871.1.i.b |
4 |
| 3871.1.j |
\(\chi_{3871}(214, \cdot)\) |
3871.1.j.a |
2 |
2 |
| 3871.1.m |
\(\chi_{3871}(1500, \cdot)\) |
3871.1.m.a |
2 |
2 |
| 3871.1.m.b |
4 |
| 3871.1.m.c |
4 |
| 3871.1.m.d |
4 |
| 3871.1.m.e |
8 |
| 3871.1.m.f |
16 |
| 3871.1.n |
\(\chi_{3871}(2157, \cdot)\) |
3871.1.n.a |
2 |
2 |
| 3871.1.o |
\(\chi_{3871}(80, \cdot)\) |
None |
0 |
2 |
| 3871.1.p |
\(\chi_{3871}(734, \cdot)\) |
None |
0 |
2 |
| 3871.1.s |
\(\chi_{3871}(1794, \cdot)\) |
3871.1.s.a |
2 |
2 |
| 3871.1.t |
\(\chi_{3871}(766, \cdot)\) |
3871.1.t.a |
2 |
2 |
| 3871.1.t.b |
4 |
| 3871.1.x |
\(\chi_{3871}(78, \cdot)\) |
None |
0 |
6 |
| 3871.1.y |
\(\chi_{3871}(475, \cdot)\) |
None |
0 |
6 |
| 3871.1.be |
\(\chi_{3871}(148, \cdot)\) |
3871.1.be.a |
12 |
12 |
| 3871.1.bf |
\(\chi_{3871}(97, \cdot)\) |
None |
0 |
12 |
| 3871.1.bk |
\(\chi_{3871}(213, \cdot)\) |
None |
0 |
12 |
| 3871.1.bl |
\(\chi_{3871}(135, \cdot)\) |
None |
0 |
12 |
| 3871.1.bo |
\(\chi_{3871}(55, \cdot)\) |
None |
0 |
12 |
| 3871.1.bp |
\(\chi_{3871}(159, \cdot)\) |
None |
0 |
12 |
| 3871.1.bq |
\(\chi_{3871}(372, \cdot)\) |
None |
0 |
12 |
| 3871.1.br |
\(\chi_{3871}(394, \cdot)\) |
None |
0 |
12 |
| 3871.1.bu |
\(\chi_{3871}(261, \cdot)\) |
None |
0 |
12 |
| 3871.1.bv |
\(\chi_{3871}(292, \cdot)\) |
None |
0 |
12 |
| 3871.1.bw |
\(\chi_{3871}(19, \cdot)\) |
3871.1.bw.a |
24 |
24 |
| 3871.1.bx |
\(\chi_{3871}(116, \cdot)\) |
3871.1.bx.a |
24 |
24 |
| 3871.1.ca |
\(\chi_{3871}(342, \cdot)\) |
None |
0 |
24 |
| 3871.1.cb |
\(\chi_{3871}(117, \cdot)\) |
3871.1.cb.a |
24 |
24 |
| 3871.1.cc |
\(\chi_{3871}(197, \cdot)\) |
3871.1.cc.a |
24 |
24 |
| 3871.1.cd |
\(\chi_{3871}(373, \cdot)\) |
3871.1.cd.a |
24 |
24 |
| 3871.1.cg |
\(\chi_{3871}(30, \cdot)\) |
3871.1.cg.a |
24 |
24 |
| 3871.1.ch |
\(\chi_{3871}(31, \cdot)\) |
3871.1.ch.a |
24 |
24 |
| 3871.1.cj |
\(\chi_{3871}(62, \cdot)\) |
None |
0 |
72 |
| 3871.1.ck |
\(\chi_{3871}(15, \cdot)\) |
None |
0 |
72 |
| 3871.1.cq |
\(\chi_{3871}(73, \cdot)\) |
None |
0 |
144 |
| 3871.1.cr |
\(\chi_{3871}(37, \cdot)\) |
None |
0 |
144 |
| 3871.1.cu |
\(\chi_{3871}(58, \cdot)\) |
None |
0 |
144 |
| 3871.1.cv |
\(\chi_{3871}(29, \cdot)\) |
None |
0 |
144 |
| 3871.1.cw |
\(\chi_{3871}(10, \cdot)\) |
None |
0 |
144 |
| 3871.1.cx |
\(\chi_{3871}(13, \cdot)\) |
None |
0 |
144 |
| 3871.1.da |
\(\chi_{3871}(86, \cdot)\) |
None |
0 |
144 |
| 3871.1.db |
\(\chi_{3871}(5, \cdot)\) |
None |
0 |
144 |
