Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4001))\).
|
Total |
New |
Old |
| Modular forms
| 669000 |
669000 |
0 |
| Cusp forms
| 665001 |
665001 |
0 |
| Eisenstein series
| 3999 |
3999 |
0 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4001))\)
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 |
| 4001.2.a |
\(\chi_{4001}(1, \cdot)\) |
4001.2.a.a |
149 |
1 |
| 4001.2.a.b |
184 |
| 4001.2.b |
\(\chi_{4001}(4000, \cdot)\) |
n/a |
332 |
1 |
| 4001.2.c |
\(\chi_{4001}(899, \cdot)\) |
n/a |
664 |
2 |
| 4001.2.d |
\(\chi_{4001}(902, \cdot)\) |
n/a |
1328 |
4 |
| 4001.2.e |
\(\chi_{4001}(70, \cdot)\) |
n/a |
1328 |
4 |
| 4001.2.f |
\(\chi_{4001}(614, \cdot)\) |
n/a |
1328 |
4 |
| 4001.2.g |
\(\chi_{4001}(1115, \cdot)\) |
n/a |
2664 |
8 |
| 4001.2.h |
\(\chi_{4001}(152, \cdot)\) |
n/a |
2656 |
8 |
| 4001.2.i |
\(\chi_{4001}(196, \cdot)\) |
n/a |
6640 |
20 |
| 4001.2.k |
\(\chi_{4001}(673, \cdot)\) |
n/a |
5312 |
16 |
| 4001.2.l |
\(\chi_{4001}(14, \cdot)\) |
n/a |
6640 |
20 |
| 4001.2.m |
\(\chi_{4001}(121, \cdot)\) |
n/a |
10656 |
32 |
| 4001.2.n |
\(\chi_{4001}(25, \cdot)\) |
n/a |
13280 |
40 |
| 4001.2.o |
\(\chi_{4001}(26, \cdot)\) |
n/a |
33200 |
100 |
| 4001.2.q |
\(\chi_{4001}(5, \cdot)\) |
n/a |
26560 |
80 |
| 4001.2.r |
\(\chi_{4001}(16, \cdot)\) |
n/a |
33200 |
100 |
| 4001.2.s |
\(\chi_{4001}(58, \cdot)\) |
n/a |
53280 |
160 |
| 4001.2.t |
\(\chi_{4001}(4, \cdot)\) |
n/a |
66400 |
200 |
| 4001.2.v |
\(\chi_{4001}(2, \cdot)\) |
n/a |
132800 |
400 |
| 4001.2.w |
\(\chi_{4001}(9, \cdot)\) |
n/a |
266400 |
800 |
"n/a" means that newforms for that character have not been added to the database yet
