# Properties

 Label 1521.2 Level 1521 Weight 2 Dimension 65715 Nonzero newspaces 30 Sturm bound 340704 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$1521 = 3^{2} \cdot 13^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$30$$ Sturm bound: $$340704$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1521))$$.

Total New Old
Modular forms 87000 67556 19444
Cusp forms 83353 65715 17638
Eisenstein series 3647 1841 1806

## Trace form

 $$65715 q - 198 q^{2} - 264 q^{3} - 198 q^{4} - 198 q^{5} - 264 q^{6} - 194 q^{7} - 180 q^{8} - 264 q^{9} + O(q^{10})$$ $$65715 q - 198 q^{2} - 264 q^{3} - 198 q^{4} - 198 q^{5} - 264 q^{6} - 194 q^{7} - 180 q^{8} - 264 q^{9} - 564 q^{10} - 186 q^{11} - 264 q^{12} - 204 q^{13} - 354 q^{14} - 264 q^{15} - 158 q^{16} - 180 q^{17} - 264 q^{18} - 554 q^{19} - 132 q^{20} - 264 q^{21} - 138 q^{22} - 174 q^{23} - 312 q^{24} - 156 q^{25} - 186 q^{26} - 504 q^{27} - 558 q^{28} - 240 q^{29} - 360 q^{30} - 258 q^{31} - 354 q^{32} - 336 q^{33} - 294 q^{34} - 354 q^{35} - 456 q^{36} - 672 q^{37} - 450 q^{38} - 336 q^{39} - 618 q^{40} - 300 q^{41} - 408 q^{42} - 218 q^{43} - 426 q^{44} - 384 q^{45} - 618 q^{46} - 258 q^{47} - 408 q^{48} - 194 q^{49} - 300 q^{50} - 312 q^{51} - 165 q^{52} - 282 q^{53} - 264 q^{54} - 462 q^{55} - 162 q^{56} - 264 q^{57} - 48 q^{58} - 114 q^{59} - 384 q^{60} - 84 q^{61} - 174 q^{62} - 360 q^{63} - 636 q^{64} - 279 q^{65} - 744 q^{66} - 278 q^{67} - 576 q^{68} - 408 q^{69} - 498 q^{70} - 462 q^{71} - 576 q^{72} - 842 q^{73} - 624 q^{74} - 504 q^{75} - 494 q^{76} - 450 q^{77} - 516 q^{78} - 450 q^{79} - 816 q^{80} - 456 q^{81} - 852 q^{82} - 522 q^{83} - 600 q^{84} - 396 q^{85} - 570 q^{86} - 456 q^{87} - 426 q^{88} - 294 q^{89} - 576 q^{90} - 646 q^{91} - 570 q^{92} - 408 q^{93} - 198 q^{94} - 174 q^{95} + 48 q^{96} - 78 q^{97} - 150 q^{98} - 120 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1521))$$

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
1521.2.a $$\chi_{1521}(1, \cdot)$$ 1521.2.a.a 1 1
1521.2.a.b 1
1521.2.a.c 1
1521.2.a.d 1
1521.2.a.e 1
1521.2.a.f 2
1521.2.a.g 2
1521.2.a.h 2
1521.2.a.i 2
1521.2.a.j 2
1521.2.a.k 2
1521.2.a.l 2
1521.2.a.m 2
1521.2.a.n 3
1521.2.a.o 3
1521.2.a.p 3
1521.2.a.q 3
1521.2.a.r 3
1521.2.a.s 3
1521.2.a.t 4
1521.2.a.u 4
1521.2.a.v 6
1521.2.a.w 6
1521.2.b $$\chi_{1521}(1351, \cdot)$$ 1521.2.b.a 2 1
1521.2.b.b 2
1521.2.b.c 2
1521.2.b.d 2
1521.2.b.e 2
1521.2.b.f 2
1521.2.b.g 4
1521.2.b.h 4
1521.2.b.i 4
1521.2.b.j 4
1521.2.b.k 6
1521.2.b.l 6
1521.2.b.m 6
1521.2.b.n 12
1521.2.e $$\chi_{1521}(508, \cdot)$$ n/a 288 2
1521.2.f $$\chi_{1521}(529, \cdot)$$ n/a 288 2
1521.2.g $$\chi_{1521}(991, \cdot)$$ n/a 120 2
1521.2.h $$\chi_{1521}(22, \cdot)$$ n/a 288 2
1521.2.i $$\chi_{1521}(746, \cdot)$$ 1521.2.i.a 4 2
1521.2.i.b 4
1521.2.i.c 8
1521.2.i.d 8
1521.2.i.e 8
1521.2.i.f 8
1521.2.i.g 12
1521.2.i.h 48
1521.2.l $$\chi_{1521}(823, \cdot)$$ n/a 288 2
1521.2.q $$\chi_{1521}(316, \cdot)$$ n/a 118 2
1521.2.r $$\chi_{1521}(868, \cdot)$$ n/a 288 2
1521.2.t $$\chi_{1521}(337, \cdot)$$ n/a 288 2
1521.2.x $$\chi_{1521}(587, \cdot)$$ n/a 576 4
1521.2.z $$\chi_{1521}(239, \cdot)$$ n/a 576 4
1521.2.ba $$\chi_{1521}(80, \cdot)$$ n/a 208 4
1521.2.bc $$\chi_{1521}(488, \cdot)$$ n/a 576 4
1521.2.be $$\chi_{1521}(118, \cdot)$$ n/a 900 12
1521.2.bh $$\chi_{1521}(64, \cdot)$$ n/a 912 12
1521.2.bi $$\chi_{1521}(16, \cdot)$$ n/a 4320 24
1521.2.bj $$\chi_{1521}(55, \cdot)$$ n/a 1776 24
1521.2.bk $$\chi_{1521}(61, \cdot)$$ n/a 4320 24
1521.2.bl $$\chi_{1521}(40, \cdot)$$ n/a 4320 24
1521.2.bn $$\chi_{1521}(8, \cdot)$$ n/a 1488 24
1521.2.bq $$\chi_{1521}(25, \cdot)$$ n/a 4320 24
1521.2.bs $$\chi_{1521}(43, \cdot)$$ n/a 4320 24
1521.2.bt $$\chi_{1521}(10, \cdot)$$ n/a 1800 24
1521.2.by $$\chi_{1521}(4, \cdot)$$ n/a 4320 24
1521.2.cb $$\chi_{1521}(20, \cdot)$$ n/a 8640 48
1521.2.cd $$\chi_{1521}(71, \cdot)$$ n/a 2880 48
1521.2.ce $$\chi_{1521}(5, \cdot)$$ n/a 8640 48
1521.2.cg $$\chi_{1521}(2, \cdot)$$ n/a 8640 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1521))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1521)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(117))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(169))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(507))$$$$^{\oplus 2}$$