## Defining parameters

 Level: $$N$$ = $$374 = 2 \cdot 11 \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$10$$ Newforms: $$29$$ Sturm bound: $$17280$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(374))$$.

Total New Old
Modular forms 4640 1409 3231
Cusp forms 4001 1409 2592
Eisenstein series 639 0 639

## Trace form

 $$1409q + 3q^{2} + 12q^{3} + 3q^{4} + 18q^{5} + 2q^{6} + 4q^{7} + 3q^{8} - q^{9} + O(q^{10})$$ $$1409q + 3q^{2} + 12q^{3} + 3q^{4} + 18q^{5} + 2q^{6} + 4q^{7} + 3q^{8} - q^{9} - 10q^{10} - 13q^{11} - 24q^{12} - 10q^{13} - 28q^{14} - 84q^{15} - 5q^{16} - 17q^{17} - 35q^{18} - 2q^{19} + 10q^{20} - 40q^{21} + 7q^{22} - 14q^{24} - 59q^{25} - 6q^{26} - 18q^{27} + 4q^{28} - 30q^{29} + 12q^{30} - 28q^{31} - 7q^{32} - 50q^{33} + 15q^{34} - 40q^{35} + 29q^{36} + 10q^{37} - 16q^{38} - 60q^{39} - 2q^{40} - 90q^{41} - 60q^{42} - 80q^{43} - 39q^{44} - 34q^{45} - 32q^{46} - 96q^{47} + 12q^{48} - 77q^{49} - 59q^{50} - 53q^{51} - 62q^{52} - 74q^{53} - 72q^{54} - 82q^{55} + 24q^{56} - 106q^{57} - 54q^{58} - 110q^{59} - 32q^{60} - 50q^{61} - 60q^{62} - 120q^{63} + 3q^{64} - 20q^{65} - 36q^{66} - 8q^{67} + 7q^{68} - 60q^{69} - 40q^{71} - 41q^{72} - 66q^{73} + 2q^{74} - 82q^{75} + 40q^{76} - 56q^{77} - 40q^{78} - 20q^{79} - 34q^{80} - 115q^{81} - 80q^{82} - 22q^{83} - 48q^{84} - 164q^{85} - 62q^{86} - 128q^{87} - 29q^{88} - 82q^{89} - 82q^{90} - 184q^{91} - 20q^{92} - 132q^{93} - 104q^{94} - 148q^{95} + 12q^{96} - 88q^{97} + 9q^{98} - 145q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(374))$$

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
374.2.a $$\chi_{374}(1, \cdot)$$ 374.2.a.a 1 1
374.2.a.b 3
374.2.a.c 3
374.2.a.d 4
374.2.a.e 4
374.2.b $$\chi_{374}(67, \cdot)$$ 374.2.b.a 6 1
374.2.b.b 8
374.2.f $$\chi_{374}(89, \cdot)$$ 374.2.f.a 12 2
374.2.f.b 16
374.2.g $$\chi_{374}(69, \cdot)$$ 374.2.g.a 4 4
374.2.g.b 4
374.2.g.c 4
374.2.g.d 8
374.2.g.e 8
374.2.g.f 16
374.2.g.g 20
374.2.h $$\chi_{374}(111, \cdot)$$ 374.2.h.a 8 4
374.2.h.b 24
374.2.h.c 32
374.2.l $$\chi_{374}(135, \cdot)$$ 374.2.l.a 32 4
374.2.l.b 40
374.2.m $$\chi_{374}(65, \cdot)$$ 374.2.m.a 72 8
374.2.m.b 72
374.2.o $$\chi_{374}(47, \cdot)$$ 374.2.o.a 64 8
374.2.o.b 80
374.2.r $$\chi_{374}(9, \cdot)$$ 374.2.r.a 128 16
374.2.r.b 160
374.2.t $$\chi_{374}(7, \cdot)$$ 374.2.t.a 288 32
374.2.t.b 288

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(374))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(374)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(187))$$$$^{\oplus 2}$$