## Defining parameters

 Level: $$N$$ = $$34 = 2 \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$4$$ Newforms: $$5$$ Sturm bound: $$144$$ Trace bound: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(34))$$.

Total New Old
Modular forms 52 11 41
Cusp forms 21 11 10
Eisenstein series 31 0 31

## Trace form

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

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$

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
34.2.a $$\chi_{34}(1, \cdot)$$ 34.2.a.a 1 1
34.2.b $$\chi_{34}(33, \cdot)$$ 34.2.b.a 2 1
34.2.c $$\chi_{34}(13, \cdot)$$ 34.2.c.a 2 2
34.2.c.b 2
34.2.d $$\chi_{34}(9, \cdot)$$ 34.2.d.a 4 4

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(34))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(34)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 2}$$