Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3200))\).
|
Total |
New |
Old |
Modular forms
| 311680 |
160248 |
151432 |
Cusp forms
| 302721 |
158280 |
144441 |
Eisenstein series
| 8959 |
1968 |
6991 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3200))\)
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 |
3200.2.a |
\(\chi_{3200}(1, \cdot)\) |
3200.2.a.a |
1 |
1 |
3200.2.a.b |
1 |
3200.2.a.c |
1 |
3200.2.a.d |
1 |
3200.2.a.e |
1 |
3200.2.a.f |
1 |
3200.2.a.g |
1 |
3200.2.a.h |
1 |
3200.2.a.i |
1 |
3200.2.a.j |
1 |
3200.2.a.k |
1 |
3200.2.a.l |
1 |
3200.2.a.m |
1 |
3200.2.a.n |
1 |
3200.2.a.o |
1 |
3200.2.a.p |
1 |
3200.2.a.q |
1 |
3200.2.a.r |
1 |
3200.2.a.s |
1 |
3200.2.a.t |
1 |
3200.2.a.u |
1 |
3200.2.a.v |
1 |
3200.2.a.w |
1 |
3200.2.a.x |
1 |
3200.2.a.y |
1 |
3200.2.a.z |
1 |
3200.2.a.ba |
1 |
3200.2.a.bb |
1 |
3200.2.a.bc |
2 |
3200.2.a.bd |
2 |
3200.2.a.be |
2 |
3200.2.a.bf |
2 |
3200.2.a.bg |
2 |
3200.2.a.bh |
2 |
3200.2.a.bi |
2 |
3200.2.a.bj |
2 |
3200.2.a.bk |
2 |
3200.2.a.bl |
2 |
3200.2.a.bm |
2 |
3200.2.a.bn |
2 |
3200.2.a.bo |
3 |
3200.2.a.bp |
3 |
3200.2.a.bq |
3 |
3200.2.a.br |
3 |
3200.2.a.bs |
3 |
3200.2.a.bt |
3 |
3200.2.a.bu |
3 |
3200.2.a.bv |
3 |
3200.2.c |
\(\chi_{3200}(2049, \cdot)\) |
3200.2.c.a |
2 |
1 |
3200.2.c.b |
2 |
3200.2.c.c |
2 |
3200.2.c.d |
2 |
3200.2.c.e |
2 |
3200.2.c.f |
2 |
3200.2.c.g |
2 |
3200.2.c.h |
2 |
3200.2.c.i |
2 |
3200.2.c.j |
2 |
3200.2.c.k |
2 |
3200.2.c.l |
2 |
3200.2.c.m |
2 |
3200.2.c.n |
2 |
3200.2.c.o |
2 |
3200.2.c.p |
2 |
3200.2.c.q |
2 |
3200.2.c.r |
2 |
3200.2.c.s |
2 |
3200.2.c.t |
2 |
3200.2.c.u |
4 |
3200.2.c.v |
4 |
3200.2.c.w |
4 |
3200.2.c.x |
4 |
3200.2.c.y |
4 |
3200.2.c.z |
4 |
3200.2.c.ba |
4 |
3200.2.c.bb |
4 |
3200.2.d |
\(\chi_{3200}(1601, \cdot)\) |
3200.2.d.a |
2 |
1 |
3200.2.d.b |
2 |
3200.2.d.c |
2 |
3200.2.d.d |
2 |
3200.2.d.e |
2 |
3200.2.d.f |
2 |
3200.2.d.g |
2 |
3200.2.d.h |
2 |
3200.2.d.i |
4 |
3200.2.d.j |
4 |
3200.2.d.k |
4 |
3200.2.d.l |
4 |
3200.2.d.m |
4 |
3200.2.d.n |
4 |
3200.2.d.o |
4 |
3200.2.d.p |
4 |
3200.2.d.q |
4 |
3200.2.d.r |
4 |
3200.2.d.s |
4 |
3200.2.d.t |
4 |
3200.2.d.u |
4 |
3200.2.d.v |
4 |
3200.2.d.w |
4 |
3200.2.f |
\(\chi_{3200}(449, \cdot)\) |
3200.2.f.a |
2 |
1 |
3200.2.f.b |
2 |
3200.2.f.c |
2 |
3200.2.f.d |
2 |
3200.2.f.e |
2 |
3200.2.f.f |
2 |
3200.2.f.g |
4 |
3200.2.f.h |
4 |
3200.2.f.i |
4 |
3200.2.f.j |
4 |
3200.2.f.k |
4 |
3200.2.f.l |
4 |
3200.2.f.m |
4 |
3200.2.f.n |
4 |
3200.2.f.o |
4 |
3200.2.f.p |
4 |
3200.2.f.q |
4 |
3200.2.f.r |
8 |
3200.2.f.s |
8 |
3200.2.j |
\(\chi_{3200}(543, \cdot)\) |
n/a |
136 |
2 |
3200.2.l |
\(\chi_{3200}(801, \cdot)\) |
n/a |
140 |
2 |
3200.2.n |
\(\chi_{3200}(1407, \cdot)\) |
n/a |
144 |
2 |
3200.2.o |
\(\chi_{3200}(1343, \cdot)\) |
n/a |
144 |
2 |
3200.2.q |
\(\chi_{3200}(1249, \cdot)\) |
n/a |
136 |
2 |
3200.2.s |
\(\chi_{3200}(2143, \cdot)\) |
n/a |
136 |
2 |
3200.2.u |
\(\chi_{3200}(641, \cdot)\) |
n/a |
480 |
4 |
3200.2.v |
\(\chi_{3200}(143, \cdot)\) |
n/a |
280 |
4 |
3200.2.y |
\(\chi_{3200}(401, \cdot)\) |
n/a |
292 |
4 |
3200.2.ba |
\(\chi_{3200}(49, \cdot)\) |
n/a |
280 |
4 |
3200.2.bb |
\(\chi_{3200}(207, \cdot)\) |
n/a |
280 |
4 |
3200.2.be |
\(\chi_{3200}(1089, \cdot)\) |
n/a |
480 |
4 |
3200.2.bg |
\(\chi_{3200}(129, \cdot)\) |
n/a |
480 |
4 |
3200.2.bj |
\(\chi_{3200}(321, \cdot)\) |
n/a |
480 |
4 |
3200.2.bl |
\(\chi_{3200}(407, \cdot)\) |
None |
0 |
8 |
3200.2.bm |
\(\chi_{3200}(201, \cdot)\) |
None |
0 |
8 |
3200.2.bn |
\(\chi_{3200}(249, \cdot)\) |
None |
0 |
8 |
3200.2.br |
\(\chi_{3200}(7, \cdot)\) |
None |
0 |
8 |
3200.2.bt |
\(\chi_{3200}(223, \cdot)\) |
n/a |
928 |
8 |
3200.2.bu |
\(\chi_{3200}(161, \cdot)\) |
n/a |
928 |
8 |
3200.2.bx |
\(\chi_{3200}(63, \cdot)\) |
n/a |
960 |
8 |
3200.2.by |
\(\chi_{3200}(127, \cdot)\) |
n/a |
960 |
8 |
3200.2.cb |
\(\chi_{3200}(289, \cdot)\) |
n/a |
928 |
8 |
3200.2.cc |
\(\chi_{3200}(1183, \cdot)\) |
n/a |
928 |
8 |
3200.2.cf |
\(\chi_{3200}(107, \cdot)\) |
n/a |
4576 |
16 |
3200.2.cg |
\(\chi_{3200}(101, \cdot)\) |
n/a |
4816 |
16 |
3200.2.ci |
\(\chi_{3200}(149, \cdot)\) |
n/a |
4576 |
16 |
3200.2.cl |
\(\chi_{3200}(43, \cdot)\) |
n/a |
4576 |
16 |
3200.2.cn |
\(\chi_{3200}(47, \cdot)\) |
n/a |
1888 |
16 |
3200.2.co |
\(\chi_{3200}(209, \cdot)\) |
n/a |
1888 |
16 |
3200.2.cq |
\(\chi_{3200}(81, \cdot)\) |
n/a |
1888 |
16 |
3200.2.ct |
\(\chi_{3200}(303, \cdot)\) |
n/a |
1888 |
16 |
3200.2.cu |
\(\chi_{3200}(23, \cdot)\) |
None |
0 |
32 |
3200.2.cy |
\(\chi_{3200}(9, \cdot)\) |
None |
0 |
32 |
3200.2.cz |
\(\chi_{3200}(41, \cdot)\) |
None |
0 |
32 |
3200.2.da |
\(\chi_{3200}(87, \cdot)\) |
None |
0 |
32 |
3200.2.dc |
\(\chi_{3200}(67, \cdot)\) |
n/a |
30592 |
64 |
3200.2.df |
\(\chi_{3200}(29, \cdot)\) |
n/a |
30592 |
64 |
3200.2.dh |
\(\chi_{3200}(21, \cdot)\) |
n/a |
30592 |
64 |
3200.2.di |
\(\chi_{3200}(3, \cdot)\) |
n/a |
30592 |
64 |
"n/a" means that newforms for that character have not been added to the database yet