# Properties

 Label 2535.2 Level 2535 Weight 2 Dimension 153084 Nonzero newspaces 40 Sturm bound 908544 Trace bound 6

## Defining parameters

 Level: $$N$$ = $$2535 = 3 \cdot 5 \cdot 13^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$40$$ Sturm bound: $$908544$$ Trace bound: $$6$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2535))$$.

Total New Old
Modular forms 230784 155540 75244
Cusp forms 223489 153084 70405
Eisenstein series 7295 2456 4839

## Trace form

 $$153084 q - 4 q^{2} - 134 q^{3} - 272 q^{4} - 398 q^{6} - 256 q^{7} + 60 q^{8} - 124 q^{9} + O(q^{10})$$ $$153084 q - 4 q^{2} - 134 q^{3} - 272 q^{4} - 398 q^{6} - 256 q^{7} + 60 q^{8} - 124 q^{9} - 340 q^{10} + 32 q^{11} - 34 q^{12} - 240 q^{13} + 72 q^{14} - 176 q^{15} - 664 q^{16} + 56 q^{17} - 40 q^{18} - 120 q^{19} + 124 q^{20} - 300 q^{21} - 56 q^{22} + 72 q^{23} - 6 q^{24} - 372 q^{25} + 120 q^{26} - 110 q^{27} + 16 q^{28} + 88 q^{29} - 152 q^{30} - 728 q^{31} + 172 q^{32} - 116 q^{33} - 128 q^{34} + 40 q^{35} - 524 q^{36} - 288 q^{37} - 64 q^{38} - 176 q^{39} - 672 q^{40} + 136 q^{41} - 84 q^{42} - 48 q^{43} + 160 q^{44} - 222 q^{45} - 384 q^{46} + 152 q^{47} - 210 q^{48} + 24 q^{49} + 176 q^{50} - 296 q^{51} - 156 q^{52} + 128 q^{53} - 230 q^{54} - 436 q^{55} + 24 q^{56} - 100 q^{57} - 184 q^{58} - 16 q^{59} - 576 q^{60} - 592 q^{61} - 144 q^{62} - 372 q^{63} - 504 q^{64} - 102 q^{65} - 1132 q^{66} - 448 q^{67} - 488 q^{68} - 468 q^{69} - 732 q^{70} - 176 q^{71} - 744 q^{72} - 456 q^{73} - 224 q^{74} - 456 q^{75} - 1064 q^{76} - 96 q^{77} - 396 q^{78} - 488 q^{79} - 92 q^{80} - 628 q^{81} - 40 q^{82} + 72 q^{83} - 276 q^{84} - 232 q^{85} + 248 q^{86} - 64 q^{87} + 360 q^{88} + 384 q^{89} - 142 q^{90} - 568 q^{91} + 504 q^{92} + 84 q^{93} + 448 q^{94} + 320 q^{95} + 2 q^{96} + 168 q^{97} + 460 q^{98} + 164 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2535))$$

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
2535.2.a $$\chi_{2535}(1, \cdot)$$ 2535.2.a.a 1 1
2535.2.a.b 1
2535.2.a.c 1
2535.2.a.d 1
2535.2.a.e 1
2535.2.a.f 1
2535.2.a.g 1
2535.2.a.h 1
2535.2.a.i 1
2535.2.a.j 1
2535.2.a.k 1
2535.2.a.l 1
2535.2.a.m 1
2535.2.a.n 2
2535.2.a.o 2
2535.2.a.p 2
2535.2.a.q 2
2535.2.a.r 2
2535.2.a.s 2
2535.2.a.t 3
2535.2.a.u 3
2535.2.a.v 3
2535.2.a.w 3
2535.2.a.x 3
2535.2.a.y 3
2535.2.a.z 3
2535.2.a.ba 3
2535.2.a.bb 3
2535.2.a.bc 3
2535.2.a.bd 3
2535.2.a.be 3
2535.2.a.bf 3
2535.2.a.bg 3
2535.2.a.bh 3
2535.2.a.bi 4
2535.2.a.bj 4
2535.2.a.bk 4
2535.2.a.bl 4
2535.2.a.bm 9
2535.2.a.bn 9
2535.2.b $$\chi_{2535}(1351, \cdot)$$ n/a 104 1
2535.2.c $$\chi_{2535}(2029, \cdot)$$ n/a 156 1
2535.2.h $$\chi_{2535}(844, \cdot)$$ n/a 152 1
2535.2.i $$\chi_{2535}(991, \cdot)$$ n/a 204 2
2535.2.k $$\chi_{2535}(1282, \cdot)$$ n/a 308 2
2535.2.m $$\chi_{2535}(677, \cdot)$$ n/a 576 2
2535.2.n $$\chi_{2535}(239, \cdot)$$ n/a 576 2
2535.2.o $$\chi_{2535}(746, \cdot)$$ n/a 408 2
2535.2.s $$\chi_{2535}(1013, \cdot)$$ n/a 576 2
2535.2.t $$\chi_{2535}(268, \cdot)$$ n/a 308 2
2535.2.v $$\chi_{2535}(2344, \cdot)$$ n/a 304 2
2535.2.ba $$\chi_{2535}(484, \cdot)$$ n/a 312 2
2535.2.bb $$\chi_{2535}(316, \cdot)$$ n/a 204 2
2535.2.bd $$\chi_{2535}(1333, \cdot)$$ n/a 616 4
2535.2.bf $$\chi_{2535}(23, \cdot)$$ n/a 1152 4
2535.2.bg $$\chi_{2535}(596, \cdot)$$ n/a 824 4
2535.2.bh $$\chi_{2535}(89, \cdot)$$ n/a 1152 4
2535.2.bl $$\chi_{2535}(653, \cdot)$$ n/a 1152 4
2535.2.bm $$\chi_{2535}(418, \cdot)$$ n/a 616 4
2535.2.bo $$\chi_{2535}(196, \cdot)$$ n/a 1440 12
2535.2.bp $$\chi_{2535}(64, \cdot)$$ n/a 2208 12
2535.2.bu $$\chi_{2535}(79, \cdot)$$ n/a 2160 12
2535.2.bv $$\chi_{2535}(181, \cdot)$$ n/a 1440 12
2535.2.bw $$\chi_{2535}(16, \cdot)$$ n/a 2928 24
2535.2.by $$\chi_{2535}(73, \cdot)$$ n/a 4368 24
2535.2.bz $$\chi_{2535}(38, \cdot)$$ n/a 8640 24
2535.2.cd $$\chi_{2535}(86, \cdot)$$ n/a 5856 24
2535.2.ce $$\chi_{2535}(44, \cdot)$$ n/a 8640 24
2535.2.cf $$\chi_{2535}(53, \cdot)$$ n/a 8640 24
2535.2.ch $$\chi_{2535}(112, \cdot)$$ n/a 4368 24
2535.2.cj $$\chi_{2535}(121, \cdot)$$ n/a 2928 24
2535.2.ck $$\chi_{2535}(94, \cdot)$$ n/a 4320 24
2535.2.cp $$\chi_{2535}(4, \cdot)$$ n/a 4416 24
2535.2.cr $$\chi_{2535}(7, \cdot)$$ n/a 8736 48
2535.2.cs $$\chi_{2535}(68, \cdot)$$ n/a 17280 48
2535.2.cw $$\chi_{2535}(59, \cdot)$$ n/a 17280 48
2535.2.cx $$\chi_{2535}(11, \cdot)$$ n/a 11616 48
2535.2.cy $$\chi_{2535}(17, \cdot)$$ n/a 17280 48
2535.2.da $$\chi_{2535}(67, \cdot)$$ n/a 8736 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2535))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2535)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(169))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(195))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(507))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(845))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2535))$$$$^{\oplus 1}$$