## Defining parameters

 Level: $$N$$ = $$103$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$4$$ Newform subspaces: $$5$$ Sturm bound: $$1768$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(103))$$.

Total New Old
Modular forms 493 493 0
Cusp forms 392 392 0
Eisenstein series 101 101 0

## Trace form

 $$392q - 48q^{2} - 47q^{3} - 44q^{4} - 45q^{5} - 39q^{6} - 43q^{7} - 36q^{8} - 38q^{9} + O(q^{10})$$ $$392q - 48q^{2} - 47q^{3} - 44q^{4} - 45q^{5} - 39q^{6} - 43q^{7} - 36q^{8} - 38q^{9} - 33q^{10} - 39q^{11} - 23q^{12} - 37q^{13} - 27q^{14} - 27q^{15} - 20q^{16} - 33q^{17} - 12q^{18} - 31q^{19} - 9q^{20} - 19q^{21} - 15q^{22} - 27q^{23} + 9q^{24} - 20q^{25} - 9q^{26} - 11q^{27} + 5q^{28} - 21q^{29} + 21q^{30} - 19q^{31} + 12q^{32} - 3q^{33} + 3q^{34} - 3q^{35} + 40q^{36} - 13q^{37} + 9q^{38} + 5q^{39} + 39q^{40} - 9q^{41} + 45q^{42} - 7q^{43} + 33q^{44} + 27q^{45} + 21q^{46} - 3q^{47} + 73q^{48} + 6q^{49} + 42q^{50} + 21q^{51} + 47q^{52} + 3q^{53} + 69q^{54} + 21q^{55} + 69q^{56} + 29q^{57} + 39q^{58} + 9q^{59} + 117q^{60} + 11q^{61} + 45q^{62} + 53q^{63} + 76q^{64} + 33q^{65} + 93q^{66} + 17q^{67} + 75q^{68} + 45q^{69} + 93q^{70} + 21q^{71} + 144q^{72} + 23q^{73} + 63q^{74} + 73q^{75} + 89q^{76} + 45q^{77} + 117q^{78} + 29q^{79} + 135q^{80} + 70q^{81} + 75q^{82} + 33q^{83} + 105q^{84} - 45q^{85} - 21q^{86} - 33q^{87} - 279q^{88} - 63q^{89} - 225q^{90} - 160q^{91} - 87q^{92} - 127q^{93} - 111q^{94} - 84q^{95} - 411q^{96} - 174q^{97} - 288q^{98} - 150q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(103))$$

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
103.2.a $$\chi_{103}(1, \cdot)$$ 103.2.a.a 2 1
103.2.a.b 6
103.2.c $$\chi_{103}(46, \cdot)$$ 103.2.c.a 16 2
103.2.e $$\chi_{103}(8, \cdot)$$ 103.2.e.a 112 16
103.2.g $$\chi_{103}(2, \cdot)$$ 103.2.g.a 256 32