Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(9251))\).
|
Total |
New |
Old |
| Modular forms
| 3544240 |
3475412 |
68828 |
| Cusp forms
| 3520161 |
3454740 |
65421 |
| Eisenstein series
| 24079 |
20672 |
3407 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(9251))\)
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 available newforms together with their dimension.
| Label |
\(\chi\) |
Newforms |
Dimension |
\(\chi\) degree |
| 9251.2.a |
\(\chi_{9251}(1, \cdot)\) |
9251.2.a.a |
1 |
1 |
| 9251.2.a.b |
1 |
| 9251.2.a.c |
1 |
| 9251.2.a.d |
1 |
| 9251.2.a.e |
3 |
| 9251.2.a.f |
4 |
| 9251.2.a.g |
4 |
| 9251.2.a.h |
4 |
| 9251.2.a.i |
4 |
| 9251.2.a.j |
4 |
| 9251.2.a.k |
6 |
| 9251.2.a.l |
6 |
| 9251.2.a.m |
7 |
| 9251.2.a.n |
8 |
| 9251.2.a.o |
9 |
| 9251.2.a.p |
9 |
| 9251.2.a.q |
12 |
| 9251.2.a.r |
12 |
| 9251.2.a.s |
18 |
| 9251.2.a.t |
18 |
| 9251.2.a.u |
26 |
| 9251.2.a.v |
26 |
| 9251.2.a.w |
39 |
| 9251.2.a.x |
39 |
| 9251.2.a.y |
39 |
| 9251.2.a.z |
39 |
| 9251.2.a.ba |
40 |
| 9251.2.a.bb |
40 |
| 9251.2.a.bc |
56 |
| 9251.2.a.bd |
56 |
| 9251.2.a.be |
72 |
| 9251.2.a.bf |
72 |
| 9251.2.b |
\(\chi_{9251}(5886, \cdot)\) |
n/a |
676 |
1 |
| 9251.2.f |
\(\chi_{9251}(5928, \cdot)\) |
n/a |
1568 |
2 |
| 9251.2.g |
\(\chi_{9251}(2524, \cdot)\) |
n/a |
3136 |
4 |
| 9251.2.h |
\(\chi_{9251}(1486, \cdot)\) |
n/a |
4044 |
6 |
| 9251.2.k |
\(\chi_{9251}(840, \cdot)\) |
n/a |
3136 |
4 |
| 9251.2.n |
\(\chi_{9251}(2333, \cdot)\) |
n/a |
4056 |
6 |
| 9251.2.o |
\(\chi_{9251}(41, \cdot)\) |
n/a |
6272 |
8 |
| 9251.2.q |
\(\chi_{9251}(901, \cdot)\) |
n/a |
9408 |
12 |
| 9251.2.s |
\(\chi_{9251}(320, \cdot)\) |
n/a |
20328 |
28 |
| 9251.2.t |
\(\chi_{9251}(190, \cdot)\) |
n/a |
18816 |
24 |
| 9251.2.w |
\(\chi_{9251}(144, \cdot)\) |
n/a |
20272 |
28 |
| 9251.2.x |
\(\chi_{9251}(196, \cdot)\) |
n/a |
18816 |
24 |
| 9251.2.ba |
\(\chi_{9251}(186, \cdot)\) |
n/a |
48608 |
56 |
| 9251.2.bd |
\(\chi_{9251}(425, \cdot)\) |
n/a |
37632 |
48 |
| 9251.2.be |
\(\chi_{9251}(59, \cdot)\) |
n/a |
97216 |
112 |
| 9251.2.bf |
\(\chi_{9251}(23, \cdot)\) |
n/a |
121968 |
168 |
| 9251.2.bg |
\(\chi_{9251}(86, \cdot)\) |
n/a |
97216 |
112 |
| 9251.2.bj |
\(\chi_{9251}(34, \cdot)\) |
n/a |
121632 |
168 |
| 9251.2.bn |
\(\chi_{9251}(17, \cdot)\) |
n/a |
194432 |
224 |
| 9251.2.bp |
\(\chi_{9251}(10, \cdot)\) |
n/a |
291648 |
336 |
| 9251.2.bq |
\(\chi_{9251}(16, \cdot)\) |
n/a |
583296 |
672 |
| 9251.2.bt |
\(\chi_{9251}(4, \cdot)\) |
n/a |
583296 |
672 |
| 9251.2.bu |
\(\chi_{9251}(2, \cdot)\) |
n/a |
1166592 |
1344 |
"n/a" means that newforms for that character have not been added to the database yet
