# Properties

 Label 1575.2 Level 1575 Weight 2 Dimension 59493 Nonzero newspaces 60 Sturm bound 345600 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$60$$ Sturm bound: $$345600$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1575))$$.

Total New Old
Modular forms 89088 61337 27751
Cusp forms 83713 59493 24220
Eisenstein series 5375 1844 3531

## Trace form

 $$59493 q - 85 q^{2} - 108 q^{3} - 105 q^{4} - 102 q^{5} - 172 q^{6} - 115 q^{7} - 195 q^{8} - 92 q^{9} + O(q^{10})$$ $$59493 q - 85 q^{2} - 108 q^{3} - 105 q^{4} - 102 q^{5} - 172 q^{6} - 115 q^{7} - 195 q^{8} - 92 q^{9} - 282 q^{10} - 106 q^{11} - 32 q^{12} - 72 q^{13} - 57 q^{14} - 296 q^{15} - 65 q^{16} - 8 q^{17} + 12 q^{18} - 200 q^{19} + 36 q^{20} - 162 q^{21} - 44 q^{22} + 46 q^{23} + 104 q^{24} - 6 q^{25} - 24 q^{26} + 6 q^{27} - 95 q^{28} + 2 q^{29} - 48 q^{30} - 26 q^{31} + 257 q^{32} - 20 q^{33} + 190 q^{34} - 76 q^{35} - 428 q^{36} - 68 q^{37} + 98 q^{38} - 168 q^{39} + 42 q^{40} - 124 q^{41} - 122 q^{42} - 164 q^{43} - 18 q^{44} - 168 q^{45} - 184 q^{46} - 86 q^{47} - 328 q^{48} - 35 q^{49} - 110 q^{50} - 332 q^{51} + 284 q^{52} + 8 q^{53} - 122 q^{54} - 124 q^{55} - 105 q^{56} - 216 q^{57} + 352 q^{58} + 148 q^{59} - 232 q^{60} + 74 q^{61} + 88 q^{62} - 180 q^{63} - 531 q^{64} - 178 q^{65} - 38 q^{66} - 12 q^{67} - 488 q^{68} - 140 q^{69} - 114 q^{70} - 152 q^{71} - 594 q^{72} - 186 q^{73} - 440 q^{74} - 448 q^{75} - 138 q^{76} - 162 q^{77} - 756 q^{78} - 108 q^{79} - 1030 q^{80} - 344 q^{81} - 406 q^{82} - 514 q^{83} - 644 q^{84} - 282 q^{85} - 634 q^{86} - 506 q^{87} - 450 q^{88} - 690 q^{89} - 752 q^{90} - 704 q^{91} - 1312 q^{92} - 578 q^{93} - 230 q^{94} - 292 q^{95} - 1016 q^{96} - 136 q^{97} - 975 q^{98} - 600 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1575))$$

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
1575.2.a $$\chi_{1575}(1, \cdot)$$ 1575.2.a.a 1 1
1575.2.a.b 1
1575.2.a.c 1
1575.2.a.d 1
1575.2.a.e 1
1575.2.a.f 1
1575.2.a.g 1
1575.2.a.h 1
1575.2.a.i 1
1575.2.a.j 1
1575.2.a.k 1
1575.2.a.l 2
1575.2.a.m 2
1575.2.a.n 2
1575.2.a.o 2
1575.2.a.p 2
1575.2.a.q 2
1575.2.a.r 2
1575.2.a.s 2
1575.2.a.t 2
1575.2.a.u 2
1575.2.a.v 2
1575.2.a.w 3
1575.2.a.x 3
1575.2.a.y 4
1575.2.a.z 4
1575.2.b $$\chi_{1575}(251, \cdot)$$ 1575.2.b.a 4 1
1575.2.b.b 4
1575.2.b.c 4
1575.2.b.d 4
1575.2.b.e 4
1575.2.b.f 8
1575.2.b.g 8
1575.2.b.h 16
1575.2.d $$\chi_{1575}(1324, \cdot)$$ 1575.2.d.a 2 1
1575.2.d.b 2
1575.2.d.c 2
1575.2.d.d 4
1575.2.d.e 4
1575.2.d.f 4
1575.2.d.g 4
1575.2.d.h 4
1575.2.d.i 4
1575.2.d.j 4
1575.2.d.k 4
1575.2.d.l 8
1575.2.g $$\chi_{1575}(1574, \cdot)$$ 1575.2.g.a 8 1
1575.2.g.b 8
1575.2.g.c 8
1575.2.g.d 8
1575.2.g.e 16
1575.2.i $$\chi_{1575}(526, \cdot)$$ n/a 228 2
1575.2.j $$\chi_{1575}(226, \cdot)$$ n/a 120 2
1575.2.k $$\chi_{1575}(1201, \cdot)$$ n/a 292 2
1575.2.l $$\chi_{1575}(151, \cdot)$$ n/a 292 2
1575.2.m $$\chi_{1575}(1268, \cdot)$$ 1575.2.m.a 8 2
1575.2.m.b 8
1575.2.m.c 12
1575.2.m.d 12
1575.2.m.e 16
1575.2.m.f 16
1575.2.p $$\chi_{1575}(118, \cdot)$$ n/a 116 2
1575.2.q $$\chi_{1575}(316, \cdot)$$ n/a 304 4
1575.2.s $$\chi_{1575}(499, \cdot)$$ n/a 280 2
1575.2.u $$\chi_{1575}(101, \cdot)$$ n/a 292 2
1575.2.v $$\chi_{1575}(299, \cdot)$$ n/a 280 2
1575.2.ba $$\chi_{1575}(524, \cdot)$$ n/a 280 2
1575.2.bc $$\chi_{1575}(899, \cdot)$$ 1575.2.bc.a 8 2
1575.2.bc.b 8
1575.2.bc.c 24
1575.2.bc.d 24
1575.2.bc.e 32
1575.2.bf $$\chi_{1575}(551, \cdot)$$ n/a 292 2
1575.2.bg $$\chi_{1575}(424, \cdot)$$ n/a 116 2
1575.2.bi $$\chi_{1575}(274, \cdot)$$ n/a 216 2
1575.2.bk $$\chi_{1575}(26, \cdot)$$ 1575.2.bk.a 4 2
1575.2.bk.b 4
1575.2.bk.c 4
1575.2.bk.d 8
1575.2.bk.e 12
1575.2.bk.f 12
1575.2.bk.g 16
1575.2.bk.h 16
1575.2.bk.i 24
1575.2.bm $$\chi_{1575}(776, \cdot)$$ n/a 292 2
1575.2.bp $$\chi_{1575}(949, \cdot)$$ n/a 280 2
1575.2.br $$\chi_{1575}(824, \cdot)$$ n/a 280 2
1575.2.bu $$\chi_{1575}(314, \cdot)$$ n/a 320 4
1575.2.bx $$\chi_{1575}(64, \cdot)$$ n/a 296 4
1575.2.bz $$\chi_{1575}(566, \cdot)$$ n/a 320 4
1575.2.ca $$\chi_{1575}(418, \cdot)$$ n/a 560 4
1575.2.cd $$\chi_{1575}(893, \cdot)$$ n/a 560 4
1575.2.cf $$\chi_{1575}(32, \cdot)$$ n/a 560 4
1575.2.ch $$\chi_{1575}(82, \cdot)$$ n/a 232 4
1575.2.cj $$\chi_{1575}(643, \cdot)$$ n/a 560 4
1575.2.ck $$\chi_{1575}(218, \cdot)$$ n/a 432 4
1575.2.cm $$\chi_{1575}(107, \cdot)$$ n/a 192 4
1575.2.co $$\chi_{1575}(157, \cdot)$$ n/a 560 4
1575.2.cq $$\chi_{1575}(121, \cdot)$$ n/a 1888 8
1575.2.cr $$\chi_{1575}(16, \cdot)$$ n/a 1888 8
1575.2.cs $$\chi_{1575}(46, \cdot)$$ n/a 784 8
1575.2.ct $$\chi_{1575}(106, \cdot)$$ n/a 1440 8
1575.2.cu $$\chi_{1575}(433, \cdot)$$ n/a 784 8
1575.2.cx $$\chi_{1575}(8, \cdot)$$ n/a 480 8
1575.2.cz $$\chi_{1575}(164, \cdot)$$ n/a 1888 8
1575.2.db $$\chi_{1575}(4, \cdot)$$ n/a 1888 8
1575.2.de $$\chi_{1575}(41, \cdot)$$ n/a 1888 8
1575.2.dg $$\chi_{1575}(206, \cdot)$$ n/a 640 8
1575.2.di $$\chi_{1575}(169, \cdot)$$ n/a 1440 8
1575.2.dk $$\chi_{1575}(109, \cdot)$$ n/a 784 8
1575.2.dl $$\chi_{1575}(236, \cdot)$$ n/a 1888 8
1575.2.do $$\chi_{1575}(89, \cdot)$$ n/a 640 8
1575.2.dq $$\chi_{1575}(104, \cdot)$$ n/a 1888 8
1575.2.dv $$\chi_{1575}(59, \cdot)$$ n/a 1888 8
1575.2.dw $$\chi_{1575}(131, \cdot)$$ n/a 1888 8
1575.2.dy $$\chi_{1575}(184, \cdot)$$ n/a 1888 8
1575.2.eb $$\chi_{1575}(187, \cdot)$$ n/a 3776 16
1575.2.ed $$\chi_{1575}(53, \cdot)$$ n/a 1280 16
1575.2.ef $$\chi_{1575}(92, \cdot)$$ n/a 2880 16
1575.2.eg $$\chi_{1575}(13, \cdot)$$ n/a 3776 16
1575.2.ei $$\chi_{1575}(73, \cdot)$$ n/a 1568 16
1575.2.ek $$\chi_{1575}(2, \cdot)$$ n/a 3776 16
1575.2.em $$\chi_{1575}(23, \cdot)$$ n/a 3776 16
1575.2.ep $$\chi_{1575}(52, \cdot)$$ n/a 3776 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1575))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1575)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(63))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(225))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(315))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(525))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1575))$$$$^{\oplus 1}$$