## Defining parameters

 Level: $$N$$ = $$1734 = 2 \cdot 3 \cdot 17^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$10$$ Sturm bound: $$332928$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(1734))$$.

Total New Old
Modular forms 84832 20663 64169
Cusp forms 81633 20663 60970
Eisenstein series 3199 0 3199

## Trace form

 $$20663q - q^{2} - q^{3} - q^{4} - 6q^{5} - q^{6} - 8q^{7} - q^{8} - q^{9} + O(q^{10})$$ $$20663q - q^{2} - q^{3} - q^{4} - 6q^{5} - q^{6} - 8q^{7} - q^{8} - q^{9} + 10q^{10} + 52q^{11} + 15q^{12} + 50q^{13} + 56q^{14} + 90q^{15} + 15q^{16} + 32q^{17} + 63q^{18} + 44q^{19} + 10q^{20} + 88q^{21} + 52q^{22} + 40q^{23} + 15q^{24} + 113q^{25} + 2q^{26} - q^{27} - 8q^{28} + 50q^{29} - 6q^{30} + 96q^{31} - q^{32} + 52q^{33} + 80q^{35} - q^{36} + 90q^{37} - 20q^{38} - 14q^{39} - 6q^{40} + 38q^{41} - 104q^{42} + 52q^{43} - 12q^{44} - 118q^{45} - 24q^{46} - 48q^{47} - q^{48} - 57q^{49} - 31q^{50} - 64q^{51} - 14q^{52} - 38q^{53} - 113q^{54} - 8q^{55} - 8q^{56} - 164q^{57} - 30q^{58} + 4q^{59} - 70q^{60} + 2q^{61} - 32q^{62} - 8q^{63} - q^{64} - 68q^{65} - 28q^{66} - 4q^{67} + 8q^{68} + 104q^{69} + 80q^{70} + 120q^{71} + 15q^{72} + 262q^{73} + 106q^{74} + 193q^{75} - 20q^{76} + 224q^{77} + 114q^{78} + 240q^{79} + 58q^{80} + 15q^{81} + 230q^{82} + 172q^{83} + 56q^{84} + 200q^{85} + 84q^{86} + 66q^{87} + 116q^{88} + 102q^{89} + 10q^{90} + 272q^{91} + 40q^{92} - 32q^{93} + 208q^{94} + 136q^{95} - q^{96} + 158q^{97} + 87q^{98} - 28q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(1734))$$

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
1734.2.a $$\chi_{1734}(1, \cdot)$$ 1734.2.a.a 1 1
1734.2.a.b 1
1734.2.a.c 1
1734.2.a.d 1
1734.2.a.e 1
1734.2.a.f 1
1734.2.a.g 1
1734.2.a.h 1
1734.2.a.i 1
1734.2.a.j 1
1734.2.a.k 1
1734.2.a.l 1
1734.2.a.m 1
1734.2.a.n 2
1734.2.a.o 2
1734.2.a.p 3
1734.2.a.q 3
1734.2.a.r 3
1734.2.a.s 3
1734.2.a.t 4
1734.2.a.u 4
1734.2.a.v 4
1734.2.a.w 4
1734.2.b $$\chi_{1734}(577, \cdot)$$ 1734.2.b.a 2 1
1734.2.b.b 2
1734.2.b.c 2
1734.2.b.d 2
1734.2.b.e 2
1734.2.b.f 2
1734.2.b.g 2
1734.2.b.h 4
1734.2.b.i 6
1734.2.b.j 6
1734.2.b.k 8
1734.2.b.l 8
1734.2.f $$\chi_{1734}(829, \cdot)$$ 1734.2.f.a 4 2
1734.2.f.b 4
1734.2.f.c 4
1734.2.f.d 4
1734.2.f.e 4
1734.2.f.f 4
1734.2.f.g 4
1734.2.f.h 4
1734.2.f.i 4
1734.2.f.j 8
1734.2.f.k 8
1734.2.f.l 8
1734.2.f.m 8
1734.2.f.n 12
1734.2.f.o 12
1734.2.h $$\chi_{1734}(733, \cdot)$$ n/a 176 4
1734.2.i $$\chi_{1734}(65, \cdot)$$ n/a 720 8
1734.2.k $$\chi_{1734}(103, \cdot)$$ n/a 800 16
1734.2.n $$\chi_{1734}(67, \cdot)$$ n/a 800 16
1734.2.o $$\chi_{1734}(13, \cdot)$$ n/a 1600 32
1734.2.q $$\chi_{1734}(19, \cdot)$$ n/a 3328 64
1734.2.t $$\chi_{1734}(5, \cdot)$$ n/a 13056 128

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(1734))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(1734)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(102))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(289))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(578))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(867))$$$$^{\oplus 2}$$