## Defining parameters

 Level: $$N$$ = $$49 = 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$4$$ Newform subspaces: $$5$$ Sturm bound: $$392$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(49))$$.

Total New Old
Modular forms 128 118 10
Cusp forms 69 69 0
Eisenstein series 59 49 10

## Trace form

 $$69q - 18q^{2} - 17q^{3} - 14q^{4} - 15q^{5} - 9q^{6} - 14q^{7} - 24q^{8} - 8q^{9} + O(q^{10})$$ $$69q - 18q^{2} - 17q^{3} - 14q^{4} - 15q^{5} - 9q^{6} - 14q^{7} - 24q^{8} - 8q^{9} - 3q^{10} - 9q^{11} + 7q^{12} - 7q^{13} - 15q^{15} + 10q^{16} - 3q^{17} + 18q^{18} - q^{19} + 21q^{20} + 7q^{21} - 3q^{22} + 3q^{23} + 39q^{24} + 10q^{25} + 21q^{26} + 19q^{27} + 28q^{28} - 9q^{29} + 51q^{30} + 11q^{31} + 42q^{32} + 27q^{33} + 33q^{34} + 21q^{35} - 2q^{36} - 11q^{37} - 3q^{38} - 14q^{39} - 57q^{40} - 21q^{41} - 21q^{42} - 37q^{43} - 63q^{44} - 48q^{45} - 75q^{46} - 15q^{47} - 72q^{48} - 56q^{49} - 51q^{50} - 33q^{51} - 77q^{52} - 9q^{53} - 27q^{54} - 54q^{55} - 42q^{56} - q^{57} - 15q^{58} - 3q^{59} + 21q^{60} - 8q^{61} + 33q^{62} + 42q^{63} + 16q^{64} + 63q^{65} + 123q^{66} + 47q^{67} + 105q^{68} + 75q^{69} + 105q^{70} + 33q^{71} + 174q^{72} + 53q^{73} + 93q^{74} + 103q^{75} + 119q^{76} + 63q^{77} + 21q^{78} + 59q^{79} + 102q^{80} + 16q^{81} - 21q^{83} - 56q^{84} - 15q^{85} - 36q^{86} - 69q^{87} - 72q^{88} - 15q^{89} - 186q^{90} - 7q^{91} - 18q^{92} - 145q^{93} - 66q^{94} - 69q^{95} - 168q^{96} - 28q^{97} - 168q^{98} - 72q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$

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
49.2.a $$\chi_{49}(1, \cdot)$$ 49.2.a.a 1 1
49.2.c $$\chi_{49}(18, \cdot)$$ 49.2.c.a 2 2
49.2.e $$\chi_{49}(8, \cdot)$$ 49.2.e.a 6 6
49.2.e.b 12
49.2.g $$\chi_{49}(2, \cdot)$$ 49.2.g.a 48 12