Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3800))\).
|
Total |
New |
Old |
| Modular forms
| 438048 |
224115 |
213933 |
| Cusp forms
| 425953 |
221327 |
204626 |
| Eisenstein series
| 12095 |
2788 |
9307 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3800))\)
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 |
| 3800.2.a |
\(\chi_{3800}(1, \cdot)\) |
3800.2.a.a |
1 |
1 |
| 3800.2.a.b |
1 |
| 3800.2.a.c |
1 |
| 3800.2.a.d |
1 |
| 3800.2.a.e |
1 |
| 3800.2.a.f |
1 |
| 3800.2.a.g |
1 |
| 3800.2.a.h |
1 |
| 3800.2.a.i |
1 |
| 3800.2.a.j |
2 |
| 3800.2.a.k |
2 |
| 3800.2.a.l |
2 |
| 3800.2.a.m |
2 |
| 3800.2.a.n |
2 |
| 3800.2.a.o |
2 |
| 3800.2.a.p |
2 |
| 3800.2.a.q |
2 |
| 3800.2.a.r |
3 |
| 3800.2.a.s |
3 |
| 3800.2.a.t |
3 |
| 3800.2.a.u |
3 |
| 3800.2.a.v |
3 |
| 3800.2.a.w |
3 |
| 3800.2.a.x |
3 |
| 3800.2.a.y |
3 |
| 3800.2.a.z |
6 |
| 3800.2.a.ba |
6 |
| 3800.2.a.bb |
6 |
| 3800.2.a.bc |
6 |
| 3800.2.a.bd |
6 |
| 3800.2.a.be |
6 |
| 3800.2.d |
\(\chi_{3800}(3649, \cdot)\) |
3800.2.d.a |
2 |
1 |
| 3800.2.d.b |
2 |
| 3800.2.d.c |
2 |
| 3800.2.d.d |
2 |
| 3800.2.d.e |
2 |
| 3800.2.d.f |
2 |
| 3800.2.d.g |
2 |
| 3800.2.d.h |
4 |
| 3800.2.d.i |
4 |
| 3800.2.d.j |
6 |
| 3800.2.d.k |
6 |
| 3800.2.d.l |
6 |
| 3800.2.d.m |
6 |
| 3800.2.d.n |
6 |
| 3800.2.d.o |
6 |
| 3800.2.d.p |
12 |
| 3800.2.d.q |
12 |
| 3800.2.e |
\(\chi_{3800}(2051, \cdot)\) |
n/a |
374 |
1 |
| 3800.2.f |
\(\chi_{3800}(1901, \cdot)\) |
n/a |
342 |
1 |
| 3800.2.g |
\(\chi_{3800}(3799, \cdot)\) |
None |
0 |
1 |
| 3800.2.j |
\(\chi_{3800}(151, \cdot)\) |
None |
0 |
1 |
| 3800.2.k |
\(\chi_{3800}(1749, \cdot)\) |
n/a |
324 |
1 |
| 3800.2.p |
\(\chi_{3800}(1899, \cdot)\) |
n/a |
356 |
1 |
| 3800.2.q |
\(\chi_{3800}(201, \cdot)\) |
n/a |
190 |
2 |
| 3800.2.t |
\(\chi_{3800}(493, \cdot)\) |
n/a |
712 |
2 |
| 3800.2.u |
\(\chi_{3800}(343, \cdot)\) |
None |
0 |
2 |
| 3800.2.v |
\(\chi_{3800}(2393, \cdot)\) |
n/a |
180 |
2 |
| 3800.2.w |
\(\chi_{3800}(2243, \cdot)\) |
n/a |
648 |
2 |
| 3800.2.z |
\(\chi_{3800}(761, \cdot)\) |
n/a |
544 |
4 |
| 3800.2.ba |
\(\chi_{3800}(349, \cdot)\) |
n/a |
712 |
2 |
| 3800.2.bb |
\(\chi_{3800}(1551, \cdot)\) |
None |
0 |
2 |
| 3800.2.bg |
\(\chi_{3800}(1699, \cdot)\) |
n/a |
712 |
2 |
| 3800.2.bj |
\(\chi_{3800}(1851, \cdot)\) |
n/a |
748 |
2 |
| 3800.2.bk |
\(\chi_{3800}(49, \cdot)\) |
n/a |
180 |
2 |
| 3800.2.bl |
\(\chi_{3800}(1399, \cdot)\) |
None |
0 |
2 |
| 3800.2.bm |
\(\chi_{3800}(501, \cdot)\) |
n/a |
748 |
2 |
| 3800.2.bp |
\(\chi_{3800}(1201, \cdot)\) |
n/a |
570 |
6 |
| 3800.2.bs |
\(\chi_{3800}(229, \cdot)\) |
n/a |
2160 |
4 |
| 3800.2.bt |
\(\chi_{3800}(911, \cdot)\) |
None |
0 |
4 |
| 3800.2.bu |
\(\chi_{3800}(379, \cdot)\) |
n/a |
2384 |
4 |
| 3800.2.bx |
\(\chi_{3800}(531, \cdot)\) |
n/a |
2384 |
4 |
| 3800.2.by |
\(\chi_{3800}(609, \cdot)\) |
n/a |
536 |
4 |
| 3800.2.cd |
\(\chi_{3800}(759, \cdot)\) |
None |
0 |
4 |
| 3800.2.ce |
\(\chi_{3800}(381, \cdot)\) |
n/a |
2160 |
4 |
| 3800.2.cf |
\(\chi_{3800}(293, \cdot)\) |
n/a |
1424 |
4 |
| 3800.2.cg |
\(\chi_{3800}(7, \cdot)\) |
None |
0 |
4 |
| 3800.2.cl |
\(\chi_{3800}(1057, \cdot)\) |
n/a |
360 |
4 |
| 3800.2.cm |
\(\chi_{3800}(843, \cdot)\) |
n/a |
1424 |
4 |
| 3800.2.cn |
\(\chi_{3800}(121, \cdot)\) |
n/a |
1200 |
8 |
| 3800.2.co |
\(\chi_{3800}(299, \cdot)\) |
n/a |
2136 |
6 |
| 3800.2.ct |
\(\chi_{3800}(101, \cdot)\) |
n/a |
2244 |
6 |
| 3800.2.cu |
\(\chi_{3800}(599, \cdot)\) |
None |
0 |
6 |
| 3800.2.cx |
\(\chi_{3800}(1049, \cdot)\) |
n/a |
540 |
6 |
| 3800.2.cy |
\(\chi_{3800}(51, \cdot)\) |
n/a |
2244 |
6 |
| 3800.2.cz |
\(\chi_{3800}(751, \cdot)\) |
None |
0 |
6 |
| 3800.2.da |
\(\chi_{3800}(149, \cdot)\) |
n/a |
2136 |
6 |
| 3800.2.df |
\(\chi_{3800}(267, \cdot)\) |
n/a |
4320 |
8 |
| 3800.2.dg |
\(\chi_{3800}(113, \cdot)\) |
n/a |
1200 |
8 |
| 3800.2.dh |
\(\chi_{3800}(647, \cdot)\) |
None |
0 |
8 |
| 3800.2.di |
\(\chi_{3800}(37, \cdot)\) |
n/a |
4768 |
8 |
| 3800.2.dl |
\(\chi_{3800}(729, \cdot)\) |
n/a |
1200 |
8 |
| 3800.2.dm |
\(\chi_{3800}(331, \cdot)\) |
n/a |
4768 |
8 |
| 3800.2.dr |
\(\chi_{3800}(581, \cdot)\) |
n/a |
4768 |
8 |
| 3800.2.ds |
\(\chi_{3800}(559, \cdot)\) |
None |
0 |
8 |
| 3800.2.dv |
\(\chi_{3800}(31, \cdot)\) |
None |
0 |
8 |
| 3800.2.dw |
\(\chi_{3800}(429, \cdot)\) |
n/a |
4768 |
8 |
| 3800.2.dx |
\(\chi_{3800}(179, \cdot)\) |
n/a |
4768 |
8 |
| 3800.2.ec |
\(\chi_{3800}(193, \cdot)\) |
n/a |
1080 |
12 |
| 3800.2.ed |
\(\chi_{3800}(43, \cdot)\) |
n/a |
4272 |
12 |
| 3800.2.eg |
\(\chi_{3800}(357, \cdot)\) |
n/a |
4272 |
12 |
| 3800.2.eh |
\(\chi_{3800}(207, \cdot)\) |
None |
0 |
12 |
| 3800.2.ei |
\(\chi_{3800}(81, \cdot)\) |
n/a |
3600 |
24 |
| 3800.2.ej |
\(\chi_{3800}(83, \cdot)\) |
n/a |
9536 |
16 |
| 3800.2.ek |
\(\chi_{3800}(217, \cdot)\) |
n/a |
2400 |
16 |
| 3800.2.ep |
\(\chi_{3800}(87, \cdot)\) |
None |
0 |
16 |
| 3800.2.eq |
\(\chi_{3800}(373, \cdot)\) |
n/a |
9536 |
16 |
| 3800.2.er |
\(\chi_{3800}(79, \cdot)\) |
None |
0 |
24 |
| 3800.2.es |
\(\chi_{3800}(61, \cdot)\) |
n/a |
14304 |
24 |
| 3800.2.ex |
\(\chi_{3800}(59, \cdot)\) |
n/a |
14304 |
24 |
| 3800.2.fa |
\(\chi_{3800}(309, \cdot)\) |
n/a |
14304 |
24 |
| 3800.2.fb |
\(\chi_{3800}(71, \cdot)\) |
None |
0 |
24 |
| 3800.2.fc |
\(\chi_{3800}(91, \cdot)\) |
n/a |
14304 |
24 |
| 3800.2.fd |
\(\chi_{3800}(9, \cdot)\) |
n/a |
3600 |
24 |
| 3800.2.fg |
\(\chi_{3800}(23, \cdot)\) |
None |
0 |
48 |
| 3800.2.fh |
\(\chi_{3800}(13, \cdot)\) |
n/a |
28608 |
48 |
| 3800.2.fk |
\(\chi_{3800}(123, \cdot)\) |
n/a |
28608 |
48 |
| 3800.2.fl |
\(\chi_{3800}(33, \cdot)\) |
n/a |
7200 |
48 |
"n/a" means that newforms for that character have not been added to the database yet
