# Properties

 Label 2576.2 Level 2576 Weight 2 Dimension 107936 Nonzero newspaces 32 Sturm bound 811008 Trace bound 9

## Defining parameters

 Level: $$N$$ = $$2576 = 2^{4} \cdot 7 \cdot 23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$32$$ Sturm bound: $$811008$$ Trace bound: $$9$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2576))$$.

Total New Old
Modular forms 206448 109828 96620
Cusp forms 199057 107936 91121
Eisenstein series 7391 1892 5499

## Trace form

 $$107936 q - 160 q^{2} - 122 q^{3} - 152 q^{4} - 198 q^{5} - 136 q^{6} - 147 q^{7} - 376 q^{8} - 38 q^{9} + O(q^{10})$$ $$107936 q - 160 q^{2} - 122 q^{3} - 152 q^{4} - 198 q^{5} - 136 q^{6} - 147 q^{7} - 376 q^{8} - 38 q^{9} - 152 q^{10} - 106 q^{11} - 168 q^{12} - 192 q^{13} - 204 q^{14} - 278 q^{15} - 184 q^{16} - 358 q^{17} - 144 q^{18} - 78 q^{19} - 136 q^{20} - 213 q^{21} - 392 q^{22} - 105 q^{23} - 328 q^{24} + 10 q^{25} - 136 q^{26} - 104 q^{27} - 180 q^{28} - 442 q^{29} - 168 q^{30} - 130 q^{31} - 120 q^{32} - 310 q^{33} - 136 q^{34} - 119 q^{35} - 408 q^{36} - 142 q^{37} - 200 q^{38} - 120 q^{39} - 184 q^{40} - 32 q^{41} - 340 q^{42} - 266 q^{43} - 264 q^{44} - 238 q^{45} - 200 q^{46} - 218 q^{47} - 360 q^{48} - 497 q^{49} - 584 q^{50} - 158 q^{51} - 384 q^{52} - 326 q^{53} - 488 q^{54} - 192 q^{55} - 380 q^{56} - 290 q^{57} - 368 q^{58} - 186 q^{59} - 488 q^{60} - 358 q^{61} - 304 q^{62} - 199 q^{63} - 560 q^{64} - 392 q^{65} - 376 q^{66} - 178 q^{67} - 272 q^{68} - 250 q^{69} - 496 q^{70} - 234 q^{71} - 328 q^{72} + 10 q^{73} - 152 q^{74} + 120 q^{75} - 104 q^{76} - 97 q^{77} - 408 q^{78} + 102 q^{79} - 120 q^{80} + 164 q^{81} - 152 q^{82} + 112 q^{83} - 212 q^{84} - 114 q^{85} - 152 q^{86} + 372 q^{87} - 120 q^{88} + 234 q^{89} - 24 q^{90} - 144 q^{91} - 452 q^{92} - 10 q^{93} - 72 q^{94} + 30 q^{95} + 24 q^{96} - 128 q^{97} - 68 q^{98} - 134 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2576))$$

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
2576.2.a $$\chi_{2576}(1, \cdot)$$ 2576.2.a.a 1 1
2576.2.a.b 1
2576.2.a.c 1
2576.2.a.d 1
2576.2.a.e 1
2576.2.a.f 1
2576.2.a.g 1
2576.2.a.h 1
2576.2.a.i 1
2576.2.a.j 1
2576.2.a.k 1
2576.2.a.l 1
2576.2.a.m 1
2576.2.a.n 1
2576.2.a.o 1
2576.2.a.p 1
2576.2.a.q 2
2576.2.a.r 2
2576.2.a.s 2
2576.2.a.t 2
2576.2.a.u 2
2576.2.a.v 3
2576.2.a.w 3
2576.2.a.x 3
2576.2.a.y 3
2576.2.a.z 4
2576.2.a.ba 4
2576.2.a.bb 5
2576.2.a.bc 5
2576.2.a.bd 5
2576.2.a.be 5
2576.2.b $$\chi_{2576}(1289, \cdot)$$ None 0 1
2576.2.e $$\chi_{2576}(1471, \cdot)$$ 2576.2.e.a 12 1
2576.2.e.b 12
2576.2.e.c 24
2576.2.e.d 24
2576.2.f $$\chi_{2576}(321, \cdot)$$ 2576.2.f.a 2 1
2576.2.f.b 4
2576.2.f.c 4
2576.2.f.d 4
2576.2.f.e 4
2576.2.f.f 12
2576.2.f.g 16
2576.2.f.h 24
2576.2.f.i 24
2576.2.i $$\chi_{2576}(2071, \cdot)$$ None 0 1
2576.2.j $$\chi_{2576}(783, \cdot)$$ 2576.2.j.a 32 1
2576.2.j.b 56
2576.2.m $$\chi_{2576}(1609, \cdot)$$ None 0 1
2576.2.n $$\chi_{2576}(183, \cdot)$$ None 0 1
2576.2.q $$\chi_{2576}(737, \cdot)$$ n/a 176 2
2576.2.s $$\chi_{2576}(139, \cdot)$$ n/a 704 2
2576.2.t $$\chi_{2576}(965, \cdot)$$ n/a 760 2
2576.2.w $$\chi_{2576}(827, \cdot)$$ n/a 576 2
2576.2.x $$\chi_{2576}(645, \cdot)$$ n/a 528 2
2576.2.ba $$\chi_{2576}(919, \cdot)$$ None 0 2
2576.2.bd $$\chi_{2576}(873, \cdot)$$ None 0 2
2576.2.be $$\chi_{2576}(47, \cdot)$$ n/a 176 2
2576.2.bh $$\chi_{2576}(1335, \cdot)$$ None 0 2
2576.2.bi $$\chi_{2576}(689, \cdot)$$ n/a 188 2
2576.2.bl $$\chi_{2576}(1103, \cdot)$$ n/a 192 2
2576.2.bm $$\chi_{2576}(921, \cdot)$$ None 0 2
2576.2.bo $$\chi_{2576}(225, \cdot)$$ n/a 720 10
2576.2.bq $$\chi_{2576}(45, \cdot)$$ n/a 1520 4
2576.2.br $$\chi_{2576}(507, \cdot)$$ n/a 1408 4
2576.2.bu $$\chi_{2576}(93, \cdot)$$ n/a 1408 4
2576.2.bv $$\chi_{2576}(275, \cdot)$$ n/a 1520 4
2576.2.bz $$\chi_{2576}(295, \cdot)$$ None 0 10
2576.2.ca $$\chi_{2576}(153, \cdot)$$ None 0 10
2576.2.cd $$\chi_{2576}(223, \cdot)$$ n/a 960 10
2576.2.ce $$\chi_{2576}(55, \cdot)$$ None 0 10
2576.2.ch $$\chi_{2576}(97, \cdot)$$ n/a 940 10
2576.2.ci $$\chi_{2576}(15, \cdot)$$ n/a 720 10
2576.2.cl $$\chi_{2576}(169, \cdot)$$ None 0 10
2576.2.cm $$\chi_{2576}(81, \cdot)$$ n/a 1880 20
2576.2.co $$\chi_{2576}(29, \cdot)$$ n/a 5760 20
2576.2.cp $$\chi_{2576}(43, \cdot)$$ n/a 5760 20
2576.2.cs $$\chi_{2576}(125, \cdot)$$ n/a 7600 20
2576.2.ct $$\chi_{2576}(27, \cdot)$$ n/a 7600 20
2576.2.cw $$\chi_{2576}(9, \cdot)$$ None 0 20
2576.2.cx $$\chi_{2576}(79, \cdot)$$ n/a 1920 20
2576.2.da $$\chi_{2576}(17, \cdot)$$ n/a 1880 20
2576.2.db $$\chi_{2576}(87, \cdot)$$ None 0 20
2576.2.de $$\chi_{2576}(31, \cdot)$$ n/a 1920 20
2576.2.df $$\chi_{2576}(89, \cdot)$$ None 0 20
2576.2.di $$\chi_{2576}(135, \cdot)$$ None 0 20
2576.2.dl $$\chi_{2576}(11, \cdot)$$ n/a 15200 40
2576.2.dm $$\chi_{2576}(165, \cdot)$$ n/a 15200 40
2576.2.dp $$\chi_{2576}(3, \cdot)$$ n/a 15200 40
2576.2.dq $$\chi_{2576}(5, \cdot)$$ n/a 15200 40

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2576))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2576)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(92))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(161))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(184))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(322))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(368))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(644))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1288))$$$$^{\oplus 2}$$