## Defining parameters

 Level: $$N$$ = $$114 = 2 \cdot 3 \cdot 19$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$6$$ Newform subspaces: $$21$$ Sturm bound: $$2880$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(114))$$.

Total New Old
Modular forms 1152 268 884
Cusp forms 1008 268 740
Eisenstein series 144 0 144

## Trace form

 $$268 q + 4 q^{2} + 6 q^{3} - 8 q^{4} - 12 q^{5} - 12 q^{6} + 32 q^{7} + 16 q^{8} - 18 q^{9} + O(q^{10})$$ $$268 q + 4 q^{2} + 6 q^{3} - 8 q^{4} - 12 q^{5} - 12 q^{6} + 32 q^{7} + 16 q^{8} - 18 q^{9} + 24 q^{10} - 24 q^{11} - 120 q^{12} - 652 q^{13} - 136 q^{14} + 252 q^{15} - 32 q^{16} + 828 q^{17} + 36 q^{18} + 1492 q^{19} + 528 q^{20} + 408 q^{21} + 372 q^{22} - 408 q^{23} - 48 q^{24} - 1550 q^{25} - 1216 q^{26} - 927 q^{27} - 736 q^{28} - 1320 q^{29} - 72 q^{30} - 4 q^{31} + 64 q^{32} + 990 q^{33} - 504 q^{34} + 2424 q^{35} - 72 q^{36} + 824 q^{37} + 40 q^{38} + 2118 q^{39} + 96 q^{40} + 816 q^{41} + 192 q^{42} + 608 q^{43} - 96 q^{44} + 2970 q^{45} + 672 q^{46} - 1716 q^{47} + 240 q^{48} - 3246 q^{49} - 356 q^{50} - 4401 q^{51} - 304 q^{52} - 396 q^{53} - 2808 q^{54} - 144 q^{55} - 256 q^{56} - 4980 q^{57} + 120 q^{58} + 1320 q^{59} - 1440 q^{60} - 544 q^{61} - 352 q^{62} - 1206 q^{63} - 128 q^{64} - 1716 q^{65} + 2304 q^{66} - 1552 q^{67} + 1008 q^{68} + 6408 q^{69} - 384 q^{70} + 396 q^{71} + 1800 q^{72} + 3290 q^{73} + 1016 q^{74} + 2616 q^{75} - 80 q^{76} - 4620 q^{77} - 6864 q^{78} - 4180 q^{79} - 192 q^{80} - 6498 q^{81} - 4296 q^{82} - 2436 q^{83} - 1248 q^{84} + 2088 q^{85} + 1376 q^{86} + 3600 q^{87} + 192 q^{88} + 1440 q^{89} + 6876 q^{90} + 5104 q^{91} + 4992 q^{92} + 11334 q^{93} + 13152 q^{94} + 10032 q^{95} - 192 q^{96} + 7196 q^{97} + 11460 q^{98} + 16551 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(114))$$

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
114.4.a $$\chi_{114}(1, \cdot)$$ 114.4.a.a 1 1
114.4.a.b 1
114.4.a.c 1
114.4.a.d 1
114.4.a.e 2
114.4.a.f 2
114.4.b $$\chi_{114}(113, \cdot)$$ 114.4.b.a 10 1
114.4.b.b 10
114.4.e $$\chi_{114}(7, \cdot)$$ 114.4.e.a 2 2
114.4.e.b 2
114.4.e.c 4
114.4.e.d 6
114.4.e.e 6
114.4.h $$\chi_{114}(65, \cdot)$$ 114.4.h.a 20 2
114.4.h.b 20
114.4.i $$\chi_{114}(25, \cdot)$$ 114.4.i.a 12 6
114.4.i.b 12
114.4.i.c 18
114.4.i.d 18
114.4.l $$\chi_{114}(29, \cdot)$$ 114.4.l.a 60 6
114.4.l.b 60

## Decomposition of $$S_{4}^{\mathrm{old}}(\Gamma_1(114))$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(\Gamma_1(114)) \cong$$ $$S_{4}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(\Gamma_1(57))$$$$^{\oplus 2}$$