# Properties

 Label 45.3 Level 45 Weight 3 Dimension 92 Nonzero newspaces 6 Newform subspaces 7 Sturm bound 432 Trace bound 4

## Defining parameters

 Level: $$N$$ = $$45 = 3^{2} \cdot 5$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$6$$ Newform subspaces: $$7$$ Sturm bound: $$432$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(45))$$.

Total New Old
Modular forms 176 120 56
Cusp forms 112 92 20
Eisenstein series 64 28 36

## Trace form

 $$92 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 10 q^{5} - 34 q^{6} - 36 q^{8} - 10 q^{9} + O(q^{10})$$ $$92 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 10 q^{5} - 34 q^{6} - 36 q^{8} - 10 q^{9} - 68 q^{10} - 50 q^{11} - 52 q^{12} - 28 q^{13} - 24 q^{14} + 4 q^{15} + 34 q^{16} + 68 q^{17} + 40 q^{18} + 20 q^{19} + 66 q^{20} - 12 q^{21} - 106 q^{22} - 28 q^{23} + 6 q^{24} - 94 q^{25} - 200 q^{26} - 164 q^{27} - 120 q^{28} - 168 q^{29} + 14 q^{30} + 120 q^{31} + 278 q^{32} + 158 q^{33} + 290 q^{34} + 392 q^{35} + 610 q^{36} + 208 q^{37} + 678 q^{38} + 400 q^{39} + 222 q^{40} + 274 q^{41} + 228 q^{42} - 142 q^{43} - 94 q^{45} - 336 q^{46} - 280 q^{47} - 682 q^{48} - 494 q^{49} - 1030 q^{50} - 658 q^{51} - 380 q^{52} - 664 q^{53} - 586 q^{54} + 4 q^{55} - 828 q^{56} - 350 q^{57} + 136 q^{58} - 366 q^{59} - 478 q^{60} - 184 q^{61} - 188 q^{62} - 108 q^{63} + 236 q^{64} + 188 q^{65} + 28 q^{66} + 222 q^{67} + 442 q^{68} + 252 q^{69} + 408 q^{70} + 520 q^{71} + 642 q^{72} + 236 q^{73} + 1044 q^{74} + 1066 q^{75} + 22 q^{76} + 952 q^{77} + 1352 q^{78} - 168 q^{79} + 1280 q^{80} + 938 q^{81} + 76 q^{82} + 908 q^{83} + 1164 q^{84} + 178 q^{85} + 1438 q^{86} + 640 q^{87} + 30 q^{88} - 278 q^{90} + 192 q^{91} - 1048 q^{92} - 972 q^{93} - 412 q^{94} - 1086 q^{95} - 1184 q^{96} - 122 q^{97} - 1688 q^{98} - 1292 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(45))$$

We only show spaces with odd 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
45.3.c $$\chi_{45}(26, \cdot)$$ 45.3.c.a 4 1
45.3.d $$\chi_{45}(44, \cdot)$$ 45.3.d.a 4 1
45.3.g $$\chi_{45}(28, \cdot)$$ 45.3.g.a 4 2
45.3.g.b 4
45.3.h $$\chi_{45}(14, \cdot)$$ 45.3.h.a 20 2
45.3.i $$\chi_{45}(11, \cdot)$$ 45.3.i.a 16 2
45.3.k $$\chi_{45}(7, \cdot)$$ 45.3.k.a 40 4

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(45))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(45)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 1}$$