# Properties

 Label 115.4 Level 115 Weight 4 Dimension 1384 Nonzero newspaces 6 Newform subspaces 12 Sturm bound 4224 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$115 = 5 \cdot 23$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$6$$ Newform subspaces: $$12$$ Sturm bound: $$4224$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(115))$$.

Total New Old
Modular forms 1672 1512 160
Cusp forms 1496 1384 112
Eisenstein series 176 128 48

## Trace form

 $$1384 q - 14 q^{2} - 26 q^{3} - 38 q^{4} - 23 q^{5} - 50 q^{6} - 34 q^{7} - 22 q^{8} + 24 q^{9} + O(q^{10})$$ $$1384 q - 14 q^{2} - 26 q^{3} - 38 q^{4} - 23 q^{5} - 50 q^{6} - 34 q^{7} - 22 q^{8} + 24 q^{9} - 73 q^{10} - 130 q^{11} - 54 q^{12} + 54 q^{13} + 26 q^{14} + 361 q^{15} + 942 q^{16} + 102 q^{17} - 382 q^{18} - 442 q^{19} - 657 q^{20} - 1410 q^{21} - 712 q^{22} - 912 q^{23} - 2684 q^{24} - 435 q^{25} - 810 q^{26} + 46 q^{27} + 586 q^{28} + 518 q^{29} + 1383 q^{30} + 1250 q^{31} + 2458 q^{32} + 1786 q^{33} + 4014 q^{34} + 1457 q^{35} + 5252 q^{36} + 1822 q^{37} + 1988 q^{38} - 134 q^{39} - 1353 q^{40} - 1210 q^{41} - 7186 q^{42} - 4338 q^{43} - 6980 q^{44} - 3222 q^{45} - 8298 q^{46} - 2800 q^{47} - 6454 q^{48} - 3764 q^{49} - 383 q^{50} - 1490 q^{51} - 74 q^{52} + 458 q^{53} + 10178 q^{54} + 4775 q^{55} + 18700 q^{56} + 11458 q^{57} + 15484 q^{58} + 6942 q^{59} + 4197 q^{60} - 86 q^{61} - 4318 q^{62} - 3926 q^{63} - 7446 q^{64} - 4725 q^{65} - 9872 q^{66} - 3178 q^{67} - 18368 q^{68} - 7346 q^{69} - 6114 q^{70} - 7710 q^{71} - 14212 q^{72} - 378 q^{73} + 148 q^{74} + 5829 q^{75} + 12612 q^{76} + 10506 q^{77} + 22294 q^{78} + 8194 q^{79} + 10426 q^{80} + 11852 q^{81} + 10054 q^{82} + 7114 q^{83} + 11710 q^{84} - 675 q^{85} + 522 q^{86} - 18566 q^{87} - 15334 q^{88} - 10942 q^{89} - 17626 q^{90} - 15604 q^{91} - 17416 q^{92} - 23108 q^{93} - 20788 q^{94} - 14763 q^{95} - 49424 q^{96} - 21518 q^{97} - 25006 q^{98} - 21650 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(115))$$

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
115.4.a $$\chi_{115}(1, \cdot)$$ 115.4.a.a 1 1
115.4.a.b 1
115.4.a.c 2
115.4.a.d 5
115.4.a.e 5
115.4.a.f 8
115.4.b $$\chi_{115}(24, \cdot)$$ 115.4.b.a 34 1
115.4.e $$\chi_{115}(22, \cdot)$$ 115.4.e.a 68 2
115.4.g $$\chi_{115}(6, \cdot)$$ 115.4.g.a 110 10
115.4.g.b 130
115.4.j $$\chi_{115}(4, \cdot)$$ 115.4.j.a 340 10
115.4.l $$\chi_{115}(7, \cdot)$$ 115.4.l.a 680 20

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(115))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(115)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(115))$$$$^{\oplus 1}$$