## Defining parameters

 Level: $$N$$ = $$23$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$2$$ Newforms: $$2$$ 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

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

## 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