## Defining parameters

 Level: $$N$$ = $$23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$2$$ Newform subspaces: $$2$$ Sturm bound: $$88$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(23))$$.

Total New Old
Modular forms 33 33 0
Cusp forms 12 12 0
Eisenstein series 21 21 0

## Trace form

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

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(23))$$

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
23.2.a $$\chi_{23}(1, \cdot)$$ 23.2.a.a 2 1
23.2.c $$\chi_{23}(2, \cdot)$$ 23.2.c.a 10 10