Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1856))\).
|
Total |
New |
Old |
Modular forms
| 109536 |
60930 |
48606 |
Cusp forms
| 105505 |
59742 |
45763 |
Eisenstein series
| 4031 |
1188 |
2843 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1856))\)
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 |
1856.2.a |
\(\chi_{1856}(1, \cdot)\) |
1856.2.a.a |
1 |
1 |
1856.2.a.b |
1 |
1856.2.a.c |
1 |
1856.2.a.d |
1 |
1856.2.a.e |
1 |
1856.2.a.f |
1 |
1856.2.a.g |
1 |
1856.2.a.h |
1 |
1856.2.a.i |
1 |
1856.2.a.j |
1 |
1856.2.a.k |
1 |
1856.2.a.l |
1 |
1856.2.a.m |
1 |
1856.2.a.n |
1 |
1856.2.a.o |
1 |
1856.2.a.p |
1 |
1856.2.a.q |
2 |
1856.2.a.r |
2 |
1856.2.a.s |
2 |
1856.2.a.t |
2 |
1856.2.a.u |
2 |
1856.2.a.v |
2 |
1856.2.a.w |
2 |
1856.2.a.x |
3 |
1856.2.a.y |
3 |
1856.2.a.z |
4 |
1856.2.a.ba |
5 |
1856.2.a.bb |
5 |
1856.2.a.bc |
6 |
1856.2.c |
\(\chi_{1856}(929, \cdot)\) |
1856.2.c.a |
8 |
1 |
1856.2.c.b |
8 |
1856.2.c.c |
20 |
1856.2.c.d |
20 |
1856.2.e |
\(\chi_{1856}(1217, \cdot)\) |
1856.2.e.a |
2 |
1 |
1856.2.e.b |
2 |
1856.2.e.c |
2 |
1856.2.e.d |
2 |
1856.2.e.e |
2 |
1856.2.e.f |
2 |
1856.2.e.g |
2 |
1856.2.e.h |
4 |
1856.2.e.i |
8 |
1856.2.e.j |
8 |
1856.2.e.k |
12 |
1856.2.e.l |
12 |
1856.2.g |
\(\chi_{1856}(289, \cdot)\) |
1856.2.g.a |
4 |
1 |
1856.2.g.b |
16 |
1856.2.g.c |
40 |
1856.2.j |
\(\chi_{1856}(911, \cdot)\) |
n/a |
116 |
2 |
1856.2.k |
\(\chi_{1856}(191, \cdot)\) |
n/a |
116 |
2 |
1856.2.m |
\(\chi_{1856}(753, \cdot)\) |
n/a |
116 |
2 |
1856.2.n |
\(\chi_{1856}(465, \cdot)\) |
n/a |
112 |
2 |
1856.2.q |
\(\chi_{1856}(1119, \cdot)\) |
n/a |
120 |
2 |
1856.2.t |
\(\chi_{1856}(655, \cdot)\) |
n/a |
116 |
2 |
1856.2.u |
\(\chi_{1856}(65, \cdot)\) |
n/a |
348 |
6 |
1856.2.v |
\(\chi_{1856}(233, \cdot)\) |
None |
0 |
4 |
1856.2.x |
\(\chi_{1856}(679, \cdot)\) |
None |
0 |
4 |
1856.2.ba |
\(\chi_{1856}(215, \cdot)\) |
None |
0 |
4 |
1856.2.bc |
\(\chi_{1856}(57, \cdot)\) |
None |
0 |
4 |
1856.2.be |
\(\chi_{1856}(33, \cdot)\) |
n/a |
360 |
6 |
1856.2.bg |
\(\chi_{1856}(129, \cdot)\) |
n/a |
348 |
6 |
1856.2.bi |
\(\chi_{1856}(161, \cdot)\) |
n/a |
360 |
6 |
1856.2.bl |
\(\chi_{1856}(307, \cdot)\) |
n/a |
1904 |
8 |
1856.2.bn |
\(\chi_{1856}(117, \cdot)\) |
n/a |
1792 |
8 |
1856.2.bp |
\(\chi_{1856}(173, \cdot)\) |
n/a |
1904 |
8 |
1856.2.bq |
\(\chi_{1856}(75, \cdot)\) |
n/a |
1904 |
8 |
1856.2.bs |
\(\chi_{1856}(47, \cdot)\) |
n/a |
696 |
12 |
1856.2.bv |
\(\chi_{1856}(31, \cdot)\) |
n/a |
720 |
12 |
1856.2.by |
\(\chi_{1856}(49, \cdot)\) |
n/a |
696 |
12 |
1856.2.bz |
\(\chi_{1856}(209, \cdot)\) |
n/a |
696 |
12 |
1856.2.cb |
\(\chi_{1856}(127, \cdot)\) |
n/a |
696 |
12 |
1856.2.cc |
\(\chi_{1856}(15, \cdot)\) |
n/a |
696 |
12 |
1856.2.cf |
\(\chi_{1856}(9, \cdot)\) |
None |
0 |
24 |
1856.2.ch |
\(\chi_{1856}(55, \cdot)\) |
None |
0 |
24 |
1856.2.ci |
\(\chi_{1856}(39, \cdot)\) |
None |
0 |
24 |
1856.2.ck |
\(\chi_{1856}(25, \cdot)\) |
None |
0 |
24 |
1856.2.cm |
\(\chi_{1856}(11, \cdot)\) |
n/a |
11424 |
48 |
1856.2.co |
\(\chi_{1856}(5, \cdot)\) |
n/a |
11424 |
48 |
1856.2.cq |
\(\chi_{1856}(45, \cdot)\) |
n/a |
11424 |
48 |
1856.2.ct |
\(\chi_{1856}(3, \cdot)\) |
n/a |
11424 |
48 |
"n/a" means that newforms for that character have not been added to the database yet