## Defining parameters

 Level: $$N$$ = $$114 = 2 \cdot 3 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$6$$ Newform subspaces: $$21$$ Sturm bound: $$1440$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(114))$$.

Total New Old
Modular forms 432 91 341
Cusp forms 289 91 198
Eisenstein series 143 0 143

## Trace form

 $$91q + q^{2} + q^{3} + q^{4} + 6q^{5} + q^{6} + 8q^{7} + q^{8} + q^{9} + O(q^{10})$$ $$91q + q^{2} + q^{3} + q^{4} + 6q^{5} + q^{6} + 8q^{7} + q^{8} + q^{9} + 6q^{10} + 12q^{11} - 5q^{12} - 34q^{13} - 28q^{14} - 30q^{15} + q^{16} - 18q^{17} + q^{18} - 65q^{19} - 30q^{20} - 34q^{21} - 42q^{22} - 12q^{23} + q^{24} - 41q^{25} - 22q^{26} - 14q^{27} - 4q^{28} - 6q^{29} + 6q^{30} - 4q^{31} + q^{32} - 42q^{33} + 18q^{34} - 24q^{35} + q^{36} + 2q^{37} + 19q^{38} - 40q^{39} + 6q^{40} + 6q^{41} + 8q^{42} - 28q^{43} + 12q^{44} + 6q^{45} + 24q^{46} + 12q^{47} + 10q^{48} + 21q^{49} + 31q^{50} + 99q^{51} + 14q^{52} + 54q^{53} + 55q^{54} + 72q^{55} + 8q^{56} + 109q^{57} + 30q^{58} + 60q^{59} + 42q^{60} + 50q^{61} + 32q^{62} + 74q^{63} + q^{64} + 48q^{65} + 84q^{66} - 4q^{67} + 18q^{68} + 78q^{69} + 48q^{70} + 36q^{71} + 10q^{72} + 20q^{73} + 38q^{74} - 11q^{75} + 19q^{76} + 24q^{77} - 22q^{78} - 76q^{79} + 6q^{80} - 71q^{81} - 30q^{82} - 60q^{83} - 46q^{84} - 36q^{85} - 28q^{86} - 150q^{87} + 12q^{88} - 54q^{89} - 84q^{90} - 80q^{91} - 48q^{92} - 118q^{93} - 96q^{94} + 6q^{95} + q^{96} - 10q^{97} - 87q^{98} - 69q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(114))$$

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
114.2.a $$\chi_{114}(1, \cdot)$$ 114.2.a.a 1 1
114.2.a.b 1
114.2.a.c 1
114.2.b $$\chi_{114}(113, \cdot)$$ 114.2.b.a 2 1
114.2.b.b 2
114.2.b.c 2
114.2.b.d 2
114.2.e $$\chi_{114}(7, \cdot)$$ 114.2.e.a 2 2
114.2.e.b 2
114.2.h $$\chi_{114}(65, \cdot)$$ 114.2.h.a 2 2
114.2.h.b 2
114.2.h.c 2
114.2.h.d 2
114.2.h.e 4
114.2.h.f 4
114.2.i $$\chi_{114}(25, \cdot)$$ 114.2.i.a 6 6
114.2.i.b 6
114.2.i.c 6
114.2.i.d 6
114.2.l $$\chi_{114}(29, \cdot)$$ 114.2.l.a 18 6
114.2.l.b 18

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(114))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(114)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 2}$$