Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3822))\).
|
Total |
New |
Old |
Modular forms
| 400896 |
93668 |
307228 |
Cusp forms
| 389377 |
93668 |
295709 |
Eisenstein series
| 11519 |
0 |
11519 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3822))\)
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 |
3822.2.a |
\(\chi_{3822}(1, \cdot)\) |
3822.2.a.a |
1 |
1 |
3822.2.a.b |
1 |
3822.2.a.c |
1 |
3822.2.a.d |
1 |
3822.2.a.e |
1 |
3822.2.a.f |
1 |
3822.2.a.g |
1 |
3822.2.a.h |
1 |
3822.2.a.i |
1 |
3822.2.a.j |
1 |
3822.2.a.k |
1 |
3822.2.a.l |
1 |
3822.2.a.m |
1 |
3822.2.a.n |
1 |
3822.2.a.o |
1 |
3822.2.a.p |
1 |
3822.2.a.q |
1 |
3822.2.a.r |
1 |
3822.2.a.s |
1 |
3822.2.a.t |
1 |
3822.2.a.u |
1 |
3822.2.a.v |
1 |
3822.2.a.w |
1 |
3822.2.a.x |
1 |
3822.2.a.y |
1 |
3822.2.a.z |
1 |
3822.2.a.ba |
1 |
3822.2.a.bb |
1 |
3822.2.a.bc |
1 |
3822.2.a.bd |
1 |
3822.2.a.be |
1 |
3822.2.a.bf |
1 |
3822.2.a.bg |
1 |
3822.2.a.bh |
1 |
3822.2.a.bi |
2 |
3822.2.a.bj |
2 |
3822.2.a.bk |
2 |
3822.2.a.bl |
2 |
3822.2.a.bm |
2 |
3822.2.a.bn |
2 |
3822.2.a.bo |
2 |
3822.2.a.bp |
2 |
3822.2.a.bq |
2 |
3822.2.a.br |
2 |
3822.2.a.bs |
2 |
3822.2.a.bt |
2 |
3822.2.a.bu |
2 |
3822.2.a.bv |
3 |
3822.2.a.bw |
3 |
3822.2.a.bx |
4 |
3822.2.a.by |
4 |
3822.2.a.bz |
4 |
3822.2.a.ca |
4 |
3822.2.c |
\(\chi_{3822}(883, \cdot)\) |
3822.2.c.a |
2 |
1 |
3822.2.c.b |
2 |
3822.2.c.c |
2 |
3822.2.c.d |
2 |
3822.2.c.e |
2 |
3822.2.c.f |
4 |
3822.2.c.g |
4 |
3822.2.c.h |
4 |
3822.2.c.i |
6 |
3822.2.c.j |
6 |
3822.2.c.k |
6 |
3822.2.c.l |
6 |
3822.2.c.m |
10 |
3822.2.c.n |
10 |
3822.2.c.o |
16 |
3822.2.c.p |
16 |
3822.2.e |
\(\chi_{3822}(3821, \cdot)\) |
n/a |
184 |
1 |
3822.2.g |
\(\chi_{3822}(2939, \cdot)\) |
n/a |
160 |
1 |
3822.2.i |
\(\chi_{3822}(79, \cdot)\) |
n/a |
160 |
2 |
3822.2.j |
\(\chi_{3822}(2713, \cdot)\) |
n/a |
188 |
2 |
3822.2.k |
\(\chi_{3822}(373, \cdot)\) |
n/a |
188 |
2 |
3822.2.l |
\(\chi_{3822}(295, \cdot)\) |
n/a |
188 |
2 |
3822.2.o |
\(\chi_{3822}(2449, \cdot)\) |
n/a |
192 |
2 |
3822.2.p |
\(\chi_{3822}(785, \cdot)\) |
n/a |
380 |
2 |
3822.2.q |
\(\chi_{3822}(881, \cdot)\) |
n/a |
376 |
2 |
3822.2.s |
\(\chi_{3822}(589, \cdot)\) |
n/a |
192 |
2 |
3822.2.u |
\(\chi_{3822}(3155, \cdot)\) |
n/a |
372 |
2 |
3822.2.z |
\(\chi_{3822}(521, \cdot)\) |
n/a |
320 |
2 |
3822.2.bb |
\(\chi_{3822}(815, \cdot)\) |
n/a |
372 |
2 |
3822.2.bd |
\(\chi_{3822}(361, \cdot)\) |
n/a |
188 |
2 |
3822.2.bg |
\(\chi_{3822}(1403, \cdot)\) |
n/a |
376 |
2 |
3822.2.bi |
\(\chi_{3822}(803, \cdot)\) |
n/a |
372 |
2 |
3822.2.bk |
\(\chi_{3822}(961, \cdot)\) |
n/a |
184 |
2 |
3822.2.bm |
\(\chi_{3822}(1843, \cdot)\) |
n/a |
188 |
2 |
3822.2.bn |
\(\chi_{3822}(2285, \cdot)\) |
n/a |
372 |
2 |
3822.2.bq |
\(\chi_{3822}(2057, \cdot)\) |
n/a |
376 |
2 |
3822.2.bs |
\(\chi_{3822}(547, \cdot)\) |
n/a |
672 |
6 |
3822.2.bv |
\(\chi_{3822}(197, \cdot)\) |
n/a |
768 |
4 |
3822.2.bw |
\(\chi_{3822}(863, \cdot)\) |
n/a |
752 |
4 |
3822.2.bx |
\(\chi_{3822}(557, \cdot)\) |
n/a |
744 |
4 |
3822.2.by |
\(\chi_{3822}(97, \cdot)\) |
n/a |
368 |
4 |
3822.2.bz |
\(\chi_{3822}(19, \cdot)\) |
n/a |
376 |
4 |
3822.2.ca |
\(\chi_{3822}(31, \cdot)\) |
n/a |
368 |
4 |
3822.2.ch |
\(\chi_{3822}(1501, \cdot)\) |
n/a |
376 |
4 |
3822.2.ci |
\(\chi_{3822}(275, \cdot)\) |
n/a |
744 |
4 |
3822.2.ck |
\(\chi_{3822}(209, \cdot)\) |
n/a |
1344 |
6 |
3822.2.cm |
\(\chi_{3822}(545, \cdot)\) |
n/a |
1584 |
6 |
3822.2.co |
\(\chi_{3822}(337, \cdot)\) |
n/a |
768 |
6 |
3822.2.cq |
\(\chi_{3822}(211, \cdot)\) |
n/a |
1584 |
12 |
3822.2.cr |
\(\chi_{3822}(445, \cdot)\) |
n/a |
1560 |
12 |
3822.2.cs |
\(\chi_{3822}(289, \cdot)\) |
n/a |
1560 |
12 |
3822.2.ct |
\(\chi_{3822}(235, \cdot)\) |
n/a |
1344 |
12 |
3822.2.cu |
\(\chi_{3822}(239, \cdot)\) |
n/a |
3168 |
12 |
3822.2.cv |
\(\chi_{3822}(265, \cdot)\) |
n/a |
1536 |
12 |
3822.2.cz |
\(\chi_{3822}(419, \cdot)\) |
n/a |
3120 |
12 |
3822.2.dc |
\(\chi_{3822}(101, \cdot)\) |
n/a |
3144 |
12 |
3822.2.dd |
\(\chi_{3822}(205, \cdot)\) |
n/a |
1560 |
12 |
3822.2.df |
\(\chi_{3822}(25, \cdot)\) |
n/a |
1584 |
12 |
3822.2.dh |
\(\chi_{3822}(17, \cdot)\) |
n/a |
3144 |
12 |
3822.2.dj |
\(\chi_{3822}(311, \cdot)\) |
n/a |
3120 |
12 |
3822.2.dm |
\(\chi_{3822}(121, \cdot)\) |
n/a |
1560 |
12 |
3822.2.do |
\(\chi_{3822}(269, \cdot)\) |
n/a |
3144 |
12 |
3822.2.dq |
\(\chi_{3822}(131, \cdot)\) |
n/a |
2688 |
12 |
3822.2.dv |
\(\chi_{3822}(185, \cdot)\) |
n/a |
3144 |
12 |
3822.2.dx |
\(\chi_{3822}(43, \cdot)\) |
n/a |
1584 |
12 |
3822.2.dz |
\(\chi_{3822}(251, \cdot)\) |
n/a |
3120 |
12 |
3822.2.ea |
\(\chi_{3822}(137, \cdot)\) |
n/a |
6288 |
24 |
3822.2.eb |
\(\chi_{3822}(145, \cdot)\) |
n/a |
3120 |
24 |
3822.2.ei |
\(\chi_{3822}(73, \cdot)\) |
n/a |
3168 |
24 |
3822.2.ej |
\(\chi_{3822}(115, \cdot)\) |
n/a |
3120 |
24 |
3822.2.ek |
\(\chi_{3822}(223, \cdot)\) |
n/a |
3168 |
24 |
3822.2.el |
\(\chi_{3822}(11, \cdot)\) |
n/a |
6288 |
24 |
3822.2.em |
\(\chi_{3822}(317, \cdot)\) |
n/a |
6240 |
24 |
3822.2.en |
\(\chi_{3822}(71, \cdot)\) |
n/a |
6240 |
24 |
"n/a" means that newforms for that character have not been added to the database yet