# Properties

 Label 2496.2 Level 2496 Weight 2 Dimension 71228 Nonzero newspaces 56 Sturm bound 688128 Trace bound 43

## Defining parameters

 Level: $$N$$ = $$2496 = 2^{6} \cdot 3 \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$56$$ Sturm bound: $$688128$$ Trace bound: $$43$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2496))$$.

Total New Old
Modular forms 175488 72196 103292
Cusp forms 168577 71228 97349
Eisenstein series 6911 968 5943

## Trace form

 $$71228 q - 60 q^{3} - 160 q^{4} - 80 q^{6} - 128 q^{7} - 100 q^{9} + O(q^{10})$$ $$71228 q - 60 q^{3} - 160 q^{4} - 80 q^{6} - 128 q^{7} - 100 q^{9} - 160 q^{10} - 16 q^{11} - 80 q^{12} - 192 q^{13} - 72 q^{15} - 160 q^{16} - 32 q^{17} - 80 q^{18} - 152 q^{19} - 72 q^{21} - 128 q^{22} - 156 q^{25} + 80 q^{26} - 108 q^{27} + 64 q^{29} + 80 q^{30} - 32 q^{31} + 160 q^{32} + 16 q^{33} + 48 q^{35} + 80 q^{36} - 96 q^{37} + 160 q^{38} - 44 q^{39} - 192 q^{40} + 64 q^{41} - 104 q^{43} + 32 q^{44} + 8 q^{45} - 160 q^{46} - 80 q^{48} - 252 q^{49} - 96 q^{50} + 72 q^{51} - 272 q^{52} - 112 q^{54} + 192 q^{55} - 224 q^{56} - 48 q^{57} - 448 q^{58} + 320 q^{59} - 272 q^{60} - 160 q^{61} - 192 q^{62} + 8 q^{63} - 544 q^{64} + 16 q^{65} - 336 q^{66} + 232 q^{67} - 192 q^{68} - 152 q^{69} - 544 q^{70} + 256 q^{71} - 80 q^{72} - 200 q^{73} - 224 q^{74} + 36 q^{75} - 416 q^{76} - 96 q^{77} - 160 q^{78} - 176 q^{79} - 96 q^{80} - 268 q^{81} - 160 q^{82} - 80 q^{83} - 304 q^{84} - 256 q^{85} - 176 q^{87} - 160 q^{88} - 64 q^{89} - 368 q^{90} - 192 q^{91} - 192 q^{93} - 160 q^{94} - 96 q^{95} - 352 q^{96} - 216 q^{97} - 176 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2496))$$

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
2496.2.a $$\chi_{2496}(1, \cdot)$$ 2496.2.a.a 1 1
2496.2.a.b 1
2496.2.a.c 1
2496.2.a.d 1
2496.2.a.e 1
2496.2.a.f 1
2496.2.a.g 1
2496.2.a.h 1
2496.2.a.i 1
2496.2.a.j 1
2496.2.a.k 1
2496.2.a.l 1
2496.2.a.m 1
2496.2.a.n 1
2496.2.a.o 1
2496.2.a.p 1
2496.2.a.q 1
2496.2.a.r 1
2496.2.a.s 1
2496.2.a.t 1
2496.2.a.u 1
2496.2.a.v 1
2496.2.a.w 1
2496.2.a.x 1
2496.2.a.y 1
2496.2.a.z 1
2496.2.a.ba 1
2496.2.a.bb 1
2496.2.a.bc 1
2496.2.a.bd 1
2496.2.a.be 2
2496.2.a.bf 2
2496.2.a.bg 2
2496.2.a.bh 2
2496.2.a.bi 2
2496.2.a.bj 2
2496.2.a.bk 3
2496.2.a.bl 3
2496.2.c $$\chi_{2496}(961, \cdot)$$ 2496.2.c.a 2 1
2496.2.c.b 2
2496.2.c.c 2
2496.2.c.d 2
2496.2.c.e 2
2496.2.c.f 2
2496.2.c.g 2
2496.2.c.h 2
2496.2.c.i 2
2496.2.c.j 2
2496.2.c.k 2
2496.2.c.l 2
2496.2.c.m 2
2496.2.c.n 2
2496.2.c.o 6
2496.2.c.p 6
2496.2.c.q 8
2496.2.c.r 8
2496.2.d $$\chi_{2496}(1535, \cdot)$$ 2496.2.d.a 2 1
2496.2.d.b 2
2496.2.d.c 2
2496.2.d.d 2
2496.2.d.e 2
2496.2.d.f 2
2496.2.d.g 2
2496.2.d.h 2
2496.2.d.i 4
2496.2.d.j 4
2496.2.d.k 4
2496.2.d.l 4
2496.2.d.m 8
2496.2.d.n 8
2496.2.d.o 12
2496.2.d.p 16
2496.2.d.q 20
2496.2.g $$\chi_{2496}(1249, \cdot)$$ 2496.2.g.a 4 1
2496.2.g.b 4
2496.2.g.c 4
2496.2.g.d 4
2496.2.g.e 8
2496.2.g.f 8
2496.2.g.g 8
2496.2.g.h 8
2496.2.h $$\chi_{2496}(1247, \cdot)$$ n/a 112 1
2496.2.j $$\chi_{2496}(287, \cdot)$$ 2496.2.j.a 4 1
2496.2.j.b 4
2496.2.j.c 12
2496.2.j.d 12
2496.2.j.e 32
2496.2.j.f 32
2496.2.m $$\chi_{2496}(2209, \cdot)$$ 2496.2.m.a 8 1
2496.2.m.b 8
2496.2.m.c 16
2496.2.m.d 24
2496.2.n $$\chi_{2496}(2495, \cdot)$$ n/a 108 1
2496.2.q $$\chi_{2496}(1153, \cdot)$$ n/a 112 2
2496.2.r $$\chi_{2496}(463, \cdot)$$ n/a 112 2
2496.2.u $$\chi_{2496}(593, \cdot)$$ n/a 216 2
2496.2.v $$\chi_{2496}(623, \cdot)$$ n/a 216 2
2496.2.x $$\chi_{2496}(625, \cdot)$$ 2496.2.x.a 40 2
2496.2.x.b 56
2496.2.bb $$\chi_{2496}(31, \cdot)$$ n/a 112 2
2496.2.bc $$\chi_{2496}(1087, \cdot)$$ n/a 112 2
2496.2.bf $$\chi_{2496}(1217, \cdot)$$ n/a 216 2
2496.2.bg $$\chi_{2496}(161, \cdot)$$ n/a 224 2
2496.2.bh $$\chi_{2496}(911, \cdot)$$ n/a 192 2
2496.2.bj $$\chi_{2496}(337, \cdot)$$ n/a 112 2
2496.2.bm $$\chi_{2496}(785, \cdot)$$ n/a 216 2
2496.2.bn $$\chi_{2496}(655, \cdot)$$ n/a 112 2
2496.2.bq $$\chi_{2496}(95, \cdot)$$ n/a 224 2
2496.2.br $$\chi_{2496}(289, \cdot)$$ n/a 112 2
2496.2.bu $$\chi_{2496}(191, \cdot)$$ n/a 216 2
2496.2.bv $$\chi_{2496}(1921, \cdot)$$ n/a 112 2
2496.2.bz $$\chi_{2496}(959, \cdot)$$ n/a 216 2
2496.2.ca $$\chi_{2496}(673, \cdot)$$ n/a 112 2
2496.2.cd $$\chi_{2496}(1439, \cdot)$$ n/a 224 2
2496.2.cf $$\chi_{2496}(473, \cdot)$$ None 0 4
2496.2.ch $$\chi_{2496}(343, \cdot)$$ None 0 4
2496.2.ci $$\chi_{2496}(25, \cdot)$$ None 0 4
2496.2.ck $$\chi_{2496}(313, \cdot)$$ None 0 4
2496.2.cn $$\chi_{2496}(599, \cdot)$$ None 0 4
2496.2.cp $$\chi_{2496}(311, \cdot)$$ None 0 4
2496.2.cq $$\chi_{2496}(281, \cdot)$$ None 0 4
2496.2.cs $$\chi_{2496}(151, \cdot)$$ None 0 4
2496.2.cu $$\chi_{2496}(305, \cdot)$$ n/a 432 4
2496.2.cx $$\chi_{2496}(175, \cdot)$$ n/a 224 4
2496.2.cz $$\chi_{2496}(49, \cdot)$$ n/a 224 4
2496.2.db $$\chi_{2496}(815, \cdot)$$ n/a 432 4
2496.2.dc $$\chi_{2496}(353, \cdot)$$ n/a 448 4
2496.2.dd $$\chi_{2496}(449, \cdot)$$ n/a 432 4
2496.2.dg $$\chi_{2496}(319, \cdot)$$ n/a 224 4
2496.2.dh $$\chi_{2496}(223, \cdot)$$ n/a 224 4
2496.2.dl $$\chi_{2496}(529, \cdot)$$ n/a 224 4
2496.2.dn $$\chi_{2496}(335, \cdot)$$ n/a 432 4
2496.2.dp $$\chi_{2496}(847, \cdot)$$ n/a 224 4
2496.2.dq $$\chi_{2496}(977, \cdot)$$ n/a 432 4
2496.2.ds $$\chi_{2496}(157, \cdot)$$ n/a 1536 8
2496.2.dt $$\chi_{2496}(155, \cdot)$$ n/a 3552 8
2496.2.dw $$\chi_{2496}(5, \cdot)$$ n/a 3552 8
2496.2.dx $$\chi_{2496}(187, \cdot)$$ n/a 1792 8
2496.2.ea $$\chi_{2496}(317, \cdot)$$ n/a 3552 8
2496.2.eb $$\chi_{2496}(499, \cdot)$$ n/a 1792 8
2496.2.ee $$\chi_{2496}(131, \cdot)$$ n/a 3072 8
2496.2.ef $$\chi_{2496}(181, \cdot)$$ n/a 1792 8
2496.2.ej $$\chi_{2496}(487, \cdot)$$ None 0 8
2496.2.el $$\chi_{2496}(41, \cdot)$$ None 0 8
2496.2.en $$\chi_{2496}(263, \cdot)$$ None 0 8
2496.2.ep $$\chi_{2496}(23, \cdot)$$ None 0 8
2496.2.eq $$\chi_{2496}(121, \cdot)$$ None 0 8
2496.2.es $$\chi_{2496}(217, \cdot)$$ None 0 8
2496.2.eu $$\chi_{2496}(7, \cdot)$$ None 0 8
2496.2.ew $$\chi_{2496}(137, \cdot)$$ None 0 8
2496.2.fa $$\chi_{2496}(179, \cdot)$$ n/a 7104 16
2496.2.fb $$\chi_{2496}(61, \cdot)$$ n/a 3584 16
2496.2.fe $$\chi_{2496}(115, \cdot)$$ n/a 3584 16
2496.2.ff $$\chi_{2496}(149, \cdot)$$ n/a 7104 16
2496.2.fi $$\chi_{2496}(19, \cdot)$$ n/a 3584 16
2496.2.fj $$\chi_{2496}(245, \cdot)$$ n/a 7104 16
2496.2.fm $$\chi_{2496}(205, \cdot)$$ n/a 3584 16
2496.2.fn $$\chi_{2496}(35, \cdot)$$ n/a 7104 16

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2496))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2496)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(48))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(96))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(192))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(208))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(312))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(416))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(624))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(832))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1248))$$$$^{\oplus 2}$$