Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3969))\).
|
Total |
New |
Old |
Modular forms
| 578016 |
436060 |
141956 |
Cusp forms
| 565057 |
430628 |
134429 |
Eisenstein series
| 12959 |
5432 |
7527 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3969))\)
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 |
3969.2.a |
\(\chi_{3969}(1, \cdot)\) |
3969.2.a.a |
1 |
1 |
3969.2.a.b |
1 |
3969.2.a.c |
1 |
3969.2.a.d |
1 |
3969.2.a.e |
1 |
3969.2.a.f |
1 |
3969.2.a.g |
2 |
3969.2.a.h |
2 |
3969.2.a.i |
2 |
3969.2.a.j |
2 |
3969.2.a.k |
2 |
3969.2.a.l |
3 |
3969.2.a.m |
3 |
3969.2.a.n |
3 |
3969.2.a.o |
3 |
3969.2.a.p |
3 |
3969.2.a.q |
3 |
3969.2.a.r |
4 |
3969.2.a.s |
4 |
3969.2.a.t |
4 |
3969.2.a.u |
4 |
3969.2.a.v |
4 |
3969.2.a.w |
4 |
3969.2.a.x |
4 |
3969.2.a.y |
4 |
3969.2.a.z |
5 |
3969.2.a.ba |
5 |
3969.2.a.bb |
5 |
3969.2.a.bc |
5 |
3969.2.a.bd |
6 |
3969.2.a.be |
6 |
3969.2.a.bf |
8 |
3969.2.a.bg |
8 |
3969.2.a.bh |
12 |
3969.2.a.bi |
12 |
3969.2.a.bj |
16 |
3969.2.c |
\(\chi_{3969}(3968, \cdot)\) |
n/a |
152 |
1 |
3969.2.e |
\(\chi_{3969}(2431, \cdot)\) |
n/a |
304 |
2 |
3969.2.f |
\(\chi_{3969}(1324, \cdot)\) |
n/a |
318 |
2 |
3969.2.g |
\(\chi_{3969}(1108, \cdot)\) |
n/a |
312 |
2 |
3969.2.h |
\(\chi_{3969}(2566, \cdot)\) |
n/a |
312 |
2 |
3969.2.i |
\(\chi_{3969}(215, \cdot)\) |
n/a |
312 |
2 |
3969.2.o |
\(\chi_{3969}(1322, \cdot)\) |
n/a |
312 |
2 |
3969.2.p |
\(\chi_{3969}(80, \cdot)\) |
n/a |
304 |
2 |
3969.2.s |
\(\chi_{3969}(2726, \cdot)\) |
n/a |
312 |
2 |
3969.2.u |
\(\chi_{3969}(568, \cdot)\) |
n/a |
1320 |
6 |
3969.2.v |
\(\chi_{3969}(361, \cdot)\) |
n/a |
696 |
6 |
3969.2.w |
\(\chi_{3969}(442, \cdot)\) |
n/a |
708 |
6 |
3969.2.x |
\(\chi_{3969}(226, \cdot)\) |
n/a |
696 |
6 |
3969.2.z |
\(\chi_{3969}(566, \cdot)\) |
n/a |
1320 |
6 |
3969.2.be |
\(\chi_{3969}(521, \cdot)\) |
n/a |
696 |
6 |
3969.2.bh |
\(\chi_{3969}(656, \cdot)\) |
n/a |
696 |
6 |
3969.2.bi |
\(\chi_{3969}(440, \cdot)\) |
n/a |
696 |
6 |
3969.2.bk |
\(\chi_{3969}(298, \cdot)\) |
n/a |
2664 |
12 |
3969.2.bl |
\(\chi_{3969}(109, \cdot)\) |
n/a |
2664 |
12 |
3969.2.bm |
\(\chi_{3969}(190, \cdot)\) |
n/a |
2664 |
12 |
3969.2.bn |
\(\chi_{3969}(163, \cdot)\) |
n/a |
2640 |
12 |
3969.2.bo |
\(\chi_{3969}(67, \cdot)\) |
n/a |
6408 |
18 |
3969.2.bp |
\(\chi_{3969}(148, \cdot)\) |
n/a |
6552 |
18 |
3969.2.bq |
\(\chi_{3969}(214, \cdot)\) |
n/a |
6408 |
18 |
3969.2.bs |
\(\chi_{3969}(26, \cdot)\) |
n/a |
2664 |
12 |
3969.2.bv |
\(\chi_{3969}(404, \cdot)\) |
n/a |
2640 |
12 |
3969.2.bw |
\(\chi_{3969}(188, \cdot)\) |
n/a |
2664 |
12 |
3969.2.cc |
\(\chi_{3969}(269, \cdot)\) |
n/a |
2664 |
12 |
3969.2.cf |
\(\chi_{3969}(362, \cdot)\) |
n/a |
6408 |
18 |
3969.2.cg |
\(\chi_{3969}(146, \cdot)\) |
n/a |
6408 |
18 |
3969.2.cl |
\(\chi_{3969}(68, \cdot)\) |
n/a |
6408 |
18 |
3969.2.cm |
\(\chi_{3969}(37, \cdot)\) |
n/a |
5976 |
36 |
3969.2.cn |
\(\chi_{3969}(64, \cdot)\) |
n/a |
5976 |
36 |
3969.2.co |
\(\chi_{3969}(100, \cdot)\) |
n/a |
5976 |
36 |
3969.2.cq |
\(\chi_{3969}(62, \cdot)\) |
n/a |
5976 |
36 |
3969.2.cr |
\(\chi_{3969}(17, \cdot)\) |
n/a |
5976 |
36 |
3969.2.cu |
\(\chi_{3969}(143, \cdot)\) |
n/a |
5976 |
36 |
3969.2.cy |
\(\chi_{3969}(25, \cdot)\) |
n/a |
54216 |
108 |
3969.2.cz |
\(\chi_{3969}(4, \cdot)\) |
n/a |
54216 |
108 |
3969.2.da |
\(\chi_{3969}(22, \cdot)\) |
n/a |
54216 |
108 |
3969.2.db |
\(\chi_{3969}(5, \cdot)\) |
n/a |
54216 |
108 |
3969.2.dg |
\(\chi_{3969}(47, \cdot)\) |
n/a |
54216 |
108 |
3969.2.dh |
\(\chi_{3969}(20, \cdot)\) |
n/a |
54216 |
108 |
"n/a" means that newforms for that character have not been added to the database yet