# Properties

 Label 103.2 Level 103 Weight 2 Dimension 392 Nonzero newspaces 4 Newform subspaces 5 Sturm bound 1768 Trace bound 1

## 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

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

## 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 available 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