# Properties

 Label 115.3 Level 115 Weight 3 Dimension 902 Nonzero newspaces 6 Newform subspaces 9 Sturm bound 3168 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$115 = 5 \cdot 23$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$6$$ Newform subspaces: $$9$$ Sturm bound: $$3168$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(115))$$.

Total New Old
Modular forms 1144 1026 118
Cusp forms 968 902 66
Eisenstein series 176 124 52

## Trace form

 $$902 q - 22 q^{2} - 22 q^{3} - 22 q^{4} - 33 q^{5} - 66 q^{6} - 22 q^{7} - 22 q^{8} - 22 q^{9} + O(q^{10})$$ $$902 q - 22 q^{2} - 22 q^{3} - 22 q^{4} - 33 q^{5} - 66 q^{6} - 22 q^{7} - 22 q^{8} - 22 q^{9} - 33 q^{10} - 66 q^{11} - 22 q^{12} - 22 q^{13} - 22 q^{14} - 110 q^{15} - 330 q^{16} - 132 q^{17} - 374 q^{18} - 88 q^{19} - 121 q^{20} - 132 q^{21} - 44 q^{22} + 22 q^{23} + 220 q^{24} + 33 q^{25} + 110 q^{26} + 308 q^{27} + 506 q^{28} + 132 q^{29} + 319 q^{30} + 132 q^{31} + 418 q^{32} + 220 q^{33} - 506 q^{34} - 253 q^{35} - 1056 q^{36} - 726 q^{37} - 792 q^{38} - 550 q^{39} - 473 q^{40} - 242 q^{41} - 682 q^{42} - 198 q^{43} - 264 q^{44} - 44 q^{45} + 110 q^{46} + 132 q^{47} + 594 q^{48} + 506 q^{49} + 77 q^{50} + 462 q^{51} + 1518 q^{52} + 330 q^{53} + 946 q^{54} + 121 q^{55} - 440 q^{56} + 308 q^{57} + 528 q^{58} - 198 q^{59} - 583 q^{60} - 682 q^{61} - 814 q^{62} - 572 q^{63} - 726 q^{64} - 264 q^{65} - 616 q^{66} - 66 q^{67} - 44 q^{68} + 88 q^{69} + 110 q^{70} + 264 q^{71} + 1232 q^{72} + 198 q^{73} + 660 q^{74} - 198 q^{75} - 308 q^{76} - 264 q^{77} - 1562 q^{78} - 110 q^{79} + 198 q^{80} - 1562 q^{81} + 22 q^{82} + 264 q^{83} - 66 q^{84} - 319 q^{85} - 374 q^{86} - 1078 q^{87} - 198 q^{88} - 286 q^{89} - 286 q^{90} - 88 q^{91} + 176 q^{92} + 484 q^{93} + 660 q^{94} + 946 q^{95} + 3960 q^{96} + 1892 q^{97} + 2618 q^{98} + 3740 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(115))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
115.3.c $$\chi_{115}(114, \cdot)$$ 115.3.c.a 1 1
115.3.c.b 1
115.3.c.c 20
115.3.d $$\chi_{115}(91, \cdot)$$ 115.3.d.a 6 1
115.3.d.b 10
115.3.f $$\chi_{115}(47, \cdot)$$ 115.3.f.a 44 2
115.3.h $$\chi_{115}(11, \cdot)$$ 115.3.h.a 160 10
115.3.i $$\chi_{115}(14, \cdot)$$ 115.3.i.a 220 10
115.3.k $$\chi_{115}(2, \cdot)$$ 115.3.k.a 440 20

## Decomposition of $$S_{3}^{\mathrm{old}}(\Gamma_1(115))$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(\Gamma_1(115)) \cong$$ $$S_{3}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 2}$$