## Defining parameters

 Level: $$N$$ = $$23$$ Weight: $$k$$ = $$3$$ Nonzero newspaces: $$2$$ Newforms: $$2$$ Sturm bound: $$132$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(\Gamma_1(23))$$.

Total New Old
Modular forms 55 55 0
Cusp forms 33 33 0
Eisenstein series 22 22 0

## Trace form

 $$33q - 11q^{2} - 11q^{3} - 11q^{4} - 11q^{5} - 11q^{6} - 11q^{7} - 11q^{8} - 11q^{9} + O(q^{10})$$ $$33q - 11q^{2} - 11q^{3} - 11q^{4} - 11q^{5} - 11q^{6} - 11q^{7} - 11q^{8} - 11q^{9} - 11q^{10} - 11q^{11} - 11q^{12} - 11q^{13} - 11q^{14} + 66q^{15} + 121q^{16} + 44q^{17} + 165q^{18} + 22q^{19} + 77q^{20} + 22q^{21} - 33q^{23} - 154q^{24} - 77q^{25} - 99q^{26} - 176q^{27} - 275q^{28} - 88q^{29} - 363q^{30} - 110q^{31} - 231q^{32} - 132q^{33} + 231q^{34} + 209q^{35} + 484q^{36} + 341q^{37} + 374q^{38} + 253q^{39} + 429q^{40} + 77q^{41} + 319q^{42} + 77q^{43} + 110q^{44} - 99q^{46} - 110q^{47} - 319q^{48} - 275q^{49} - 396q^{50} - 275q^{51} - 781q^{52} - 187q^{53} - 495q^{54} - 165q^{55} + 176q^{56} - 176q^{57} - 286q^{58} + 77q^{59} + 539q^{60} + 297q^{61} + 385q^{62} + 264q^{63} + 341q^{64} + 220q^{65} + 264q^{66} + 11q^{67} - 66q^{69} - 198q^{70} - 176q^{71} - 638q^{72} - 121q^{73} - 352q^{74} + 154q^{75} + 110q^{76} + 110q^{77} + 759q^{78} + 33q^{79} - 242q^{80} + 737q^{81} - 33q^{82} - 154q^{83} + 11q^{84} + 275q^{85} + 143q^{86} + 517q^{87} + 429q^{88} + 121q^{89} + 242q^{90} - 110q^{92} - 286q^{93} - 352q^{94} - 154q^{95} - 440q^{96} + 154q^{97} + 77q^{98} - 242q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(\Gamma_1(23))$$

We only show spaces with odd 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
23.3.b $$\chi_{23}(22, \cdot)$$ 23.3.b.a 3 1
23.3.d $$\chi_{23}(5, \cdot)$$ 23.3.d.a 30 10