Defining parameters
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(855))\).
|
Total |
New |
Old |
Modular forms
| 27072 |
19166 |
7906 |
Cusp forms
| 24769 |
18246 |
6523 |
Eisenstein series
| 2303 |
920 |
1383 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(855))\)
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 |
855.2.a |
\(\chi_{855}(1, \cdot)\) |
855.2.a.a |
1 |
1 |
855.2.a.b |
1 |
855.2.a.c |
1 |
855.2.a.d |
2 |
855.2.a.e |
2 |
855.2.a.f |
2 |
855.2.a.g |
2 |
855.2.a.h |
3 |
855.2.a.i |
3 |
855.2.a.j |
3 |
855.2.a.k |
3 |
855.2.a.l |
3 |
855.2.a.m |
4 |
855.2.b |
\(\chi_{855}(854, \cdot)\) |
855.2.b.a |
4 |
1 |
855.2.b.b |
4 |
855.2.b.c |
8 |
855.2.b.d |
24 |
855.2.c |
\(\chi_{855}(514, \cdot)\) |
855.2.c.a |
2 |
1 |
855.2.c.b |
2 |
855.2.c.c |
2 |
855.2.c.d |
6 |
855.2.c.e |
6 |
855.2.c.f |
12 |
855.2.c.g |
14 |
855.2.h |
\(\chi_{855}(341, \cdot)\) |
855.2.h.a |
24 |
1 |
855.2.i |
\(\chi_{855}(286, \cdot)\) |
855.2.i.a |
26 |
2 |
855.2.i.b |
30 |
855.2.i.c |
42 |
855.2.i.d |
46 |
855.2.j |
\(\chi_{855}(106, \cdot)\) |
855.2.j.a |
80 |
2 |
855.2.j.b |
80 |
855.2.k |
\(\chi_{855}(406, \cdot)\) |
855.2.k.a |
2 |
2 |
855.2.k.b |
2 |
855.2.k.c |
2 |
855.2.k.d |
2 |
855.2.k.e |
4 |
855.2.k.f |
4 |
855.2.k.g |
6 |
855.2.k.h |
8 |
855.2.k.i |
10 |
855.2.k.j |
12 |
855.2.k.k |
12 |
855.2.l |
\(\chi_{855}(391, \cdot)\) |
855.2.l.a |
80 |
2 |
855.2.l.b |
80 |
855.2.n |
\(\chi_{855}(647, \cdot)\) |
855.2.n.a |
4 |
2 |
855.2.n.b |
4 |
855.2.n.c |
8 |
855.2.n.d |
20 |
855.2.n.e |
36 |
855.2.p |
\(\chi_{855}(37, \cdot)\) |
855.2.p.a |
4 |
2 |
855.2.p.b |
4 |
855.2.p.c |
4 |
855.2.p.d |
4 |
855.2.p.e |
8 |
855.2.p.f |
12 |
855.2.p.g |
24 |
855.2.p.h |
36 |
855.2.s |
\(\chi_{855}(49, \cdot)\) |
855.2.s.a |
232 |
2 |
855.2.t |
\(\chi_{855}(164, \cdot)\) |
855.2.t.a |
232 |
2 |
855.2.w |
\(\chi_{855}(56, \cdot)\) |
855.2.w.a |
160 |
2 |
855.2.x |
\(\chi_{855}(221, \cdot)\) |
855.2.x.a |
160 |
2 |
855.2.bc |
\(\chi_{855}(521, \cdot)\) |
855.2.bc.a |
48 |
2 |
855.2.bd |
\(\chi_{855}(179, \cdot)\) |
855.2.bd.a |
16 |
2 |
855.2.bd.b |
64 |
855.2.be |
\(\chi_{855}(64, \cdot)\) |
855.2.be.a |
4 |
2 |
855.2.be.b |
8 |
855.2.be.c |
8 |
855.2.be.d |
12 |
855.2.be.e |
24 |
855.2.be.f |
40 |
855.2.bj |
\(\chi_{855}(229, \cdot)\) |
855.2.bj.a |
108 |
2 |
855.2.bj.b |
108 |
855.2.bk |
\(\chi_{855}(619, \cdot)\) |
855.2.bk.a |
232 |
2 |
855.2.bl |
\(\chi_{855}(284, \cdot)\) |
855.2.bl.a |
32 |
2 |
855.2.bl.b |
200 |
855.2.bm |
\(\chi_{855}(734, \cdot)\) |
855.2.bm.a |
232 |
2 |
855.2.bp |
\(\chi_{855}(506, \cdot)\) |
855.2.bp.a |
160 |
2 |
855.2.bs |
\(\chi_{855}(226, \cdot)\) |
855.2.bs.a |
12 |
6 |
855.2.bs.b |
18 |
855.2.bs.c |
18 |
855.2.bs.d |
18 |
855.2.bs.e |
24 |
855.2.bs.f |
30 |
855.2.bs.g |
42 |
855.2.bs.h |
42 |
855.2.bt |
\(\chi_{855}(61, \cdot)\) |
855.2.bt.a |
240 |
6 |
855.2.bt.b |
240 |
855.2.bu |
\(\chi_{855}(16, \cdot)\) |
855.2.bu.a |
240 |
6 |
855.2.bu.b |
240 |
855.2.bv |
\(\chi_{855}(88, \cdot)\) |
855.2.bv.a |
464 |
4 |
855.2.bx |
\(\chi_{855}(68, \cdot)\) |
855.2.bx.a |
464 |
4 |
855.2.bz |
\(\chi_{855}(197, \cdot)\) |
855.2.bz.a |
160 |
4 |
855.2.cc |
\(\chi_{855}(322, \cdot)\) |
855.2.cc.a |
464 |
4 |
855.2.ce |
\(\chi_{855}(202, \cdot)\) |
855.2.ce.a |
464 |
4 |
855.2.cg |
\(\chi_{855}(77, \cdot)\) |
855.2.cg.a |
4 |
4 |
855.2.cg.b |
4 |
855.2.cg.c |
208 |
855.2.cg.d |
216 |
855.2.ci |
\(\chi_{855}(182, \cdot)\) |
855.2.ci.a |
464 |
4 |
855.2.cj |
\(\chi_{855}(217, \cdot)\) |
855.2.cj.a |
4 |
4 |
855.2.cj.b |
4 |
855.2.cj.c |
4 |
855.2.cj.d |
4 |
855.2.cj.e |
24 |
855.2.cj.f |
72 |
855.2.cj.g |
80 |
855.2.cn |
\(\chi_{855}(4, \cdot)\) |
855.2.cn.a |
696 |
6 |
855.2.co |
\(\chi_{855}(299, \cdot)\) |
855.2.co.a |
696 |
6 |
855.2.cp |
\(\chi_{855}(41, \cdot)\) |
855.2.cp.a |
480 |
6 |
855.2.cq |
\(\chi_{855}(71, \cdot)\) |
855.2.cq.a |
168 |
6 |
855.2.cz |
\(\chi_{855}(14, \cdot)\) |
855.2.cz.a |
696 |
6 |
855.2.da |
\(\chi_{855}(199, \cdot)\) |
855.2.da.a |
24 |
6 |
855.2.da.b |
48 |
855.2.da.c |
96 |
855.2.da.d |
120 |
855.2.db |
\(\chi_{855}(89, \cdot)\) |
855.2.db.a |
240 |
6 |
855.2.dc |
\(\chi_{855}(454, \cdot)\) |
855.2.dc.a |
696 |
6 |
855.2.dd |
\(\chi_{855}(86, \cdot)\) |
855.2.dd.a |
480 |
6 |
855.2.dh |
\(\chi_{855}(47, \cdot)\) |
855.2.dh.a |
1392 |
12 |
855.2.dk |
\(\chi_{855}(13, \cdot)\) |
855.2.dk.a |
1392 |
12 |
855.2.dl |
\(\chi_{855}(127, \cdot)\) |
855.2.dl.a |
96 |
12 |
855.2.dl.b |
240 |
855.2.dl.c |
240 |
855.2.dm |
\(\chi_{855}(23, \cdot)\) |
855.2.dm.a |
1392 |
12 |
855.2.dn |
\(\chi_{855}(17, \cdot)\) |
855.2.dn.a |
480 |
12 |
855.2.dq |
\(\chi_{855}(22, \cdot)\) |
855.2.dq.a |
1392 |
12 |