# Properties

 Label 2496.4 Level 2496 Weight 4 Dimension 214652 Nonzero newspaces 56 Sturm bound 1376256 Trace bound 43

## Defining parameters

 Level: $$N$$ = $$2496 = 2^{6} \cdot 3 \cdot 13$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$56$$ Sturm bound: $$1376256$$ Trace bound: $$43$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(2496))$$.

Total New Old
Modular forms 519552 215620 303932
Cusp forms 512640 214652 297988
Eisenstein series 6912 968 5944

## Trace form

 $$214652 q - 60 q^{3} - 160 q^{4} - 80 q^{6} - 128 q^{7} - 100 q^{9} + O(q^{10})$$ $$214652 q - 60 q^{3} - 160 q^{4} - 80 q^{6} - 128 q^{7} - 100 q^{9} - 160 q^{10} - 80 q^{11} - 80 q^{12} - 32 q^{13} + 184 q^{15} - 160 q^{16} + 416 q^{17} - 80 q^{18} - 24 q^{19} - 104 q^{21} + 1728 q^{22} + 1920 q^{24} + 4 q^{25} - 80 q^{26} - 396 q^{27} - 3200 q^{28} - 1600 q^{29} - 4720 q^{30} - 1568 q^{31} - 4960 q^{32} - 1808 q^{33} - 4160 q^{34} - 912 q^{35} - 1840 q^{36} - 224 q^{37} + 1760 q^{38} + 532 q^{39} + 6208 q^{40} + 3776 q^{41} + 6240 q^{42} + 1496 q^{43} + 4000 q^{44} - 1048 q^{45} - 160 q^{46} - 80 q^{48} + 1092 q^{49} - 11424 q^{50} + 6088 q^{51} - 6800 q^{52} - 944 q^{54} + 2752 q^{55} + 1568 q^{56} + 496 q^{57} + 9344 q^{58} - 13760 q^{59} + 9712 q^{60} - 160 q^{61} + 11712 q^{62} - 5112 q^{63} + 24032 q^{64} - 4048 q^{65} + 10896 q^{66} - 24216 q^{67} + 8256 q^{68} - 1784 q^{69} + 7904 q^{70} - 1792 q^{71} - 80 q^{72} + 3896 q^{73} - 10528 q^{74} + 13892 q^{75} - 23968 q^{76} + 7008 q^{77} - 12208 q^{78} + 34384 q^{79} - 20064 q^{80} - 2572 q^{81} - 160 q^{82} + 5360 q^{83} - 8368 q^{84} + 4544 q^{85} + 2512 q^{87} - 160 q^{88} - 704 q^{89} + 18640 q^{90} - 3200 q^{91} + 256 q^{93} - 160 q^{94} - 15456 q^{95} + 25760 q^{96} - 13720 q^{97} + 1616 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(2496))$$

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
2496.4.a $$\chi_{2496}(1, \cdot)$$ 2496.4.a.a 1 1
2496.4.a.b 1
2496.4.a.c 1
2496.4.a.d 1
2496.4.a.e 1
2496.4.a.f 1
2496.4.a.g 1
2496.4.a.h 1
2496.4.a.i 1
2496.4.a.j 1
2496.4.a.k 1
2496.4.a.l 1
2496.4.a.m 1
2496.4.a.n 1
2496.4.a.o 1
2496.4.a.p 1
2496.4.a.q 1
2496.4.a.r 1
2496.4.a.s 2
2496.4.a.t 2
2496.4.a.u 2
2496.4.a.v 2
2496.4.a.w 2
2496.4.a.x 2
2496.4.a.y 2
2496.4.a.z 2
2496.4.a.ba 2
2496.4.a.bb 2
2496.4.a.bc 2
2496.4.a.bd 2
2496.4.a.be 2
2496.4.a.bf 2
2496.4.a.bg 2
2496.4.a.bh 2
2496.4.a.bi 2
2496.4.a.bj 2
2496.4.a.bk 3
2496.4.a.bl 3
2496.4.a.bm 3
2496.4.a.bn 3
2496.4.a.bo 3
2496.4.a.bp 3
2496.4.a.bq 3
2496.4.a.br 3
2496.4.a.bs 4
2496.4.a.bt 4
2496.4.a.bu 4
2496.4.a.bv 4
2496.4.a.bw 5
2496.4.a.bx 5
2496.4.a.by 5
2496.4.a.bz 5
2496.4.a.ca 5
2496.4.a.cb 5
2496.4.a.cc 5
2496.4.a.cd 5
2496.4.a.ce 5
2496.4.a.cf 5
2496.4.c $$\chi_{2496}(961, \cdot)$$ n/a 168 1
2496.4.d $$\chi_{2496}(1535, \cdot)$$ n/a 288 1
2496.4.g $$\chi_{2496}(1249, \cdot)$$ n/a 144 1
2496.4.h $$\chi_{2496}(1247, \cdot)$$ n/a 336 1
2496.4.j $$\chi_{2496}(287, \cdot)$$ n/a 288 1
2496.4.m $$\chi_{2496}(2209, \cdot)$$ n/a 168 1
2496.4.n $$\chi_{2496}(2495, \cdot)$$ n/a 332 1
2496.4.q $$\chi_{2496}(1153, \cdot)$$ n/a 336 2
2496.4.r $$\chi_{2496}(463, \cdot)$$ n/a 336 2
2496.4.u $$\chi_{2496}(593, \cdot)$$ n/a 664 2
2496.4.v $$\chi_{2496}(623, \cdot)$$ n/a 664 2
2496.4.x $$\chi_{2496}(625, \cdot)$$ n/a 288 2
2496.4.bb $$\chi_{2496}(31, \cdot)$$ n/a 336 2
2496.4.bc $$\chi_{2496}(1087, \cdot)$$ n/a 336 2
2496.4.bf $$\chi_{2496}(1217, \cdot)$$ n/a 664 2
2496.4.bg $$\chi_{2496}(161, \cdot)$$ n/a 672 2
2496.4.bh $$\chi_{2496}(911, \cdot)$$ n/a 576 2
2496.4.bj $$\chi_{2496}(337, \cdot)$$ n/a 336 2
2496.4.bm $$\chi_{2496}(785, \cdot)$$ n/a 664 2
2496.4.bn $$\chi_{2496}(655, \cdot)$$ n/a 336 2
2496.4.bq $$\chi_{2496}(95, \cdot)$$ n/a 672 2
2496.4.br $$\chi_{2496}(289, \cdot)$$ n/a 336 2
2496.4.bu $$\chi_{2496}(191, \cdot)$$ n/a 664 2
2496.4.bv $$\chi_{2496}(1921, \cdot)$$ n/a 336 2
2496.4.bz $$\chi_{2496}(959, \cdot)$$ n/a 664 2
2496.4.ca $$\chi_{2496}(673, \cdot)$$ n/a 336 2
2496.4.cd $$\chi_{2496}(1439, \cdot)$$ n/a 672 2
2496.4.cf $$\chi_{2496}(473, \cdot)$$ None 0 4
2496.4.ch $$\chi_{2496}(343, \cdot)$$ None 0 4
2496.4.ci $$\chi_{2496}(25, \cdot)$$ None 0 4
2496.4.ck $$\chi_{2496}(313, \cdot)$$ None 0 4
2496.4.cn $$\chi_{2496}(599, \cdot)$$ None 0 4
2496.4.cp $$\chi_{2496}(311, \cdot)$$ None 0 4
2496.4.cq $$\chi_{2496}(281, \cdot)$$ None 0 4
2496.4.cs $$\chi_{2496}(151, \cdot)$$ None 0 4
2496.4.cu $$\chi_{2496}(305, \cdot)$$ n/a 1328 4
2496.4.cx $$\chi_{2496}(175, \cdot)$$ n/a 672 4
2496.4.cz $$\chi_{2496}(49, \cdot)$$ n/a 672 4
2496.4.db $$\chi_{2496}(815, \cdot)$$ n/a 1328 4
2496.4.dc $$\chi_{2496}(353, \cdot)$$ n/a 1344 4
2496.4.dd $$\chi_{2496}(449, \cdot)$$ n/a 1328 4
2496.4.dg $$\chi_{2496}(319, \cdot)$$ n/a 672 4
2496.4.dh $$\chi_{2496}(223, \cdot)$$ n/a 672 4
2496.4.dl $$\chi_{2496}(529, \cdot)$$ n/a 672 4
2496.4.dn $$\chi_{2496}(335, \cdot)$$ n/a 1328 4
2496.4.dp $$\chi_{2496}(847, \cdot)$$ n/a 672 4
2496.4.dq $$\chi_{2496}(977, \cdot)$$ n/a 1328 4
2496.4.ds $$\chi_{2496}(157, \cdot)$$ n/a 4608 8
2496.4.dt $$\chi_{2496}(155, \cdot)$$ n/a 10720 8
2496.4.dw $$\chi_{2496}(5, \cdot)$$ n/a 10720 8
2496.4.dx $$\chi_{2496}(187, \cdot)$$ n/a 5376 8
2496.4.ea $$\chi_{2496}(317, \cdot)$$ n/a 10720 8
2496.4.eb $$\chi_{2496}(499, \cdot)$$ n/a 5376 8
2496.4.ee $$\chi_{2496}(131, \cdot)$$ n/a 9216 8
2496.4.ef $$\chi_{2496}(181, \cdot)$$ n/a 5376 8
2496.4.ej $$\chi_{2496}(487, \cdot)$$ None 0 8
2496.4.el $$\chi_{2496}(41, \cdot)$$ None 0 8
2496.4.en $$\chi_{2496}(263, \cdot)$$ None 0 8
2496.4.ep $$\chi_{2496}(23, \cdot)$$ None 0 8
2496.4.eq $$\chi_{2496}(121, \cdot)$$ None 0 8
2496.4.es $$\chi_{2496}(217, \cdot)$$ None 0 8
2496.4.eu $$\chi_{2496}(7, \cdot)$$ None 0 8
2496.4.ew $$\chi_{2496}(137, \cdot)$$ None 0 8
2496.4.fa $$\chi_{2496}(179, \cdot)$$ n/a 21440 16
2496.4.fb $$\chi_{2496}(61, \cdot)$$ n/a 10752 16
2496.4.fe $$\chi_{2496}(115, \cdot)$$ n/a 10752 16
2496.4.ff $$\chi_{2496}(149, \cdot)$$ n/a 21440 16
2496.4.fi $$\chi_{2496}(19, \cdot)$$ n/a 10752 16
2496.4.fj $$\chi_{2496}(245, \cdot)$$ n/a 21440 16
2496.4.fm $$\chi_{2496}(205, \cdot)$$ n/a 10752 16
2496.4.fn $$\chi_{2496}(35, \cdot)$$ n/a 21440 16

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

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(2496))$$ into lower level spaces

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