## Defining parameters

 Level: $$N$$ = $$2738 = 2 \cdot 37^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$12$$ Sturm bound: $$936396$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(2738))$$.

Total New Old
Modular forms 236079 77920 158159
Cusp forms 232120 77920 154200
Eisenstein series 3959 0 3959

## Trace form

 $$77920 q + q^{2} + 4 q^{3} + q^{4} + 6 q^{5} + 4 q^{6} + 8 q^{7} + q^{8} + 13 q^{9} + O(q^{10})$$ $$77920 q + q^{2} + 4 q^{3} + q^{4} + 6 q^{5} + 4 q^{6} + 8 q^{7} + q^{8} + 13 q^{9} + 6 q^{10} + 12 q^{11} + 4 q^{12} + 14 q^{13} + 8 q^{14} + 24 q^{15} + q^{16} + 18 q^{17} + 13 q^{18} + 20 q^{19} + 6 q^{20} + 32 q^{21} + 12 q^{22} + 24 q^{23} + 4 q^{24} + 31 q^{25} - 4 q^{26} - 56 q^{27} - 16 q^{28} - 42 q^{29} - 120 q^{30} - 184 q^{31} + q^{32} - 96 q^{33} - 126 q^{34} - 168 q^{35} - 77 q^{36} - 84 q^{37} - 52 q^{38} - 112 q^{39} - 84 q^{40} - 174 q^{41} - 112 q^{42} - 100 q^{43} + 12 q^{44} - 138 q^{45} - 120 q^{46} - 24 q^{47} - 20 q^{48} - 39 q^{49} + 13 q^{50} + 72 q^{51} + 14 q^{52} + 54 q^{53} + 40 q^{54} + 72 q^{55} + 8 q^{56} + 80 q^{57} + 30 q^{58} - 12 q^{59} + 24 q^{60} - 28 q^{61} + 32 q^{62} - 112 q^{63} + q^{64} - 78 q^{65} + 48 q^{66} - 4 q^{67} + 18 q^{68} - 192 q^{69} + 48 q^{70} - 72 q^{71} + 13 q^{72} - 70 q^{73} - 236 q^{75} + 20 q^{76} - 48 q^{77} + 56 q^{78} - 64 q^{79} + 6 q^{80} - 167 q^{81} + 42 q^{82} + 12 q^{83} + 32 q^{84} - 54 q^{85} + 44 q^{86} - 96 q^{87} + 12 q^{88} + 78 q^{90} + 16 q^{91} - 48 q^{92} - 88 q^{93} - 96 q^{94} - 168 q^{95} + 4 q^{96} - 190 q^{97} - 231 q^{98} - 204 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(2738))$$

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
2738.2.a $$\chi_{2738}(1, \cdot)$$ 2738.2.a.a 1 1
2738.2.a.b 1
2738.2.a.c 1
2738.2.a.d 1
2738.2.a.e 2
2738.2.a.f 2
2738.2.a.g 2
2738.2.a.h 2
2738.2.a.i 2
2738.2.a.j 2
2738.2.a.k 2
2738.2.a.l 2
2738.2.a.m 3
2738.2.a.n 3
2738.2.a.o 3
2738.2.a.p 3
2738.2.a.q 6
2738.2.a.r 6
2738.2.a.s 6
2738.2.a.t 6
2738.2.a.u 9
2738.2.a.v 9
2738.2.a.w 18
2738.2.a.x 18
2738.2.b $$\chi_{2738}(2737, \cdot)$$ n/a 110 1
2738.2.c $$\chi_{2738}(581, \cdot)$$ n/a 218 2
2738.2.e $$\chi_{2738}(1951, \cdot)$$ n/a 220 2
2738.2.f $$\chi_{2738}(737, \cdot)$$ n/a 666 6
2738.2.h $$\chi_{2738}(437, \cdot)$$ n/a 672 6
2738.2.j $$\chi_{2738}(75, \cdot)$$ n/a 4284 36
2738.2.k $$\chi_{2738}(73, \cdot)$$ n/a 4248 36
2738.2.l $$\chi_{2738}(47, \cdot)$$ n/a 8568 72
2738.2.n $$\chi_{2738}(11, \cdot)$$ n/a 8496 72
2738.2.o $$\chi_{2738}(7, \cdot)$$ n/a 25272 216
2738.2.q $$\chi_{2738}(3, \cdot)$$ n/a 25056 216

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(2738))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(2738)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(37))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(74))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1369))$$$$^{\oplus 2}$$