## Defining parameters

 Level: $$N$$ = $$1334 = 2 \cdot 23 \cdot 29$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Sturm bound: $$221760$$ Trace bound: $$4$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1334))$$.

Total New Old
Modular forms 56672 18369 38303
Cusp forms 54209 18369 35840
Eisenstein series 2463 0 2463

## Trace form

 $$18369q + 3q^{2} + 12q^{3} + 3q^{4} + 18q^{5} + 12q^{6} + 24q^{7} + 3q^{8} + 39q^{9} + O(q^{10})$$ $$18369q + 3q^{2} + 12q^{3} + 3q^{4} + 18q^{5} + 12q^{6} + 24q^{7} + 3q^{8} + 39q^{9} + 18q^{10} + 36q^{11} + 12q^{12} + 42q^{13} + 24q^{14} + 28q^{15} + 3q^{16} + 10q^{17} - 49q^{18} + 16q^{19} - 40q^{20} - 148q^{21} - 64q^{22} - 69q^{23} - 44q^{24} - 107q^{25} - 72q^{26} - 180q^{27} - 20q^{28} - 75q^{29} - 184q^{30} - 60q^{31} + 3q^{32} - 68q^{33} - 16q^{34} - 12q^{35} - 17q^{36} - 30q^{37} + 4q^{38} - 32q^{39} + 4q^{40} + 82q^{41} + 96q^{42} + 44q^{43} + 36q^{44} + 32q^{45} + 47q^{46} + 12q^{48} - 73q^{49} + 93q^{50} + 16q^{51} + 42q^{52} - 8q^{53} + 76q^{54} - 184q^{55} - 20q^{56} - 92q^{57} + 15q^{58} - 96q^{59} + 28q^{60} - 102q^{61} - 36q^{62} - 132q^{63} + 3q^{64} - 182q^{65} - 32q^{66} + 4q^{67} - 34q^{68} - 88q^{69} - 88q^{70} - 228q^{71} - 49q^{72} - 48q^{73} - 230q^{74} - 260q^{75} - 52q^{76} - 212q^{77} - 188q^{78} - 92q^{79} - 26q^{80} - 349q^{81} - 74q^{82} - 148q^{83} - 116q^{84} - 144q^{85} - 192q^{86} - 110q^{87} + 36q^{88} - 54q^{89} - 46q^{90} - 88q^{91} - 37q^{92} + 160q^{93} + 32q^{94} - 220q^{95} + 12q^{96} - 8q^{97} - 141q^{98} - 276q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1334))$$

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
1334.2.a $$\chi_{1334}(1, \cdot)$$ 1334.2.a.a 1 1
1334.2.a.b 1
1334.2.a.c 1
1334.2.a.d 4
1334.2.a.e 4
1334.2.a.f 5
1334.2.a.g 5
1334.2.a.h 5
1334.2.a.i 8
1334.2.a.j 9
1334.2.a.k 10
1334.2.c $$\chi_{1334}(231, \cdot)$$ 1334.2.c.a 28 1
1334.2.c.b 28
1334.2.f $$\chi_{1334}(505, \cdot)$$ n/a 120 2
1334.2.g $$\chi_{1334}(139, \cdot)$$ n/a 324 6
1334.2.h $$\chi_{1334}(59, \cdot)$$ n/a 560 10
1334.2.j $$\chi_{1334}(93, \cdot)$$ n/a 336 6
1334.2.m $$\chi_{1334}(173, \cdot)$$ n/a 600 10
1334.2.o $$\chi_{1334}(137, \cdot)$$ n/a 720 12
1334.2.q $$\chi_{1334}(17, \cdot)$$ n/a 1200 20
1334.2.s $$\chi_{1334}(25, \cdot)$$ n/a 3600 60
1334.2.u $$\chi_{1334}(9, \cdot)$$ n/a 3600 60
1334.2.x $$\chi_{1334}(11, \cdot)$$ n/a 7200 120

"n/a" means that newforms for that character have not been added to the database yet

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1334))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1334)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(29))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(46))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(58))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(667))$$$$^{\oplus 2}$$