# Properties

 Label 23.4 Level 23 Weight 4 Dimension 55 Nonzero newspaces 2 Newform subspaces 3 Sturm bound 176 Trace bound 1

## Defining parameters

 Level: $$N$$ = $$23$$ Weight: $$k$$ = $$4$$ Nonzero newspaces: $$2$$ Newform subspaces: $$3$$ Sturm bound: $$176$$ Trace bound: $$1$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(\Gamma_1(23))$$.

Total New Old
Modular forms 77 75 2
Cusp forms 55 55 0
Eisenstein series 22 20 2

## Trace form

 $$55 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} + O(q^{10})$$ $$55 q - 11 q^{2} - 11 q^{3} - 11 q^{4} - 11 q^{5} - 11 q^{6} - 11 q^{7} - 11 q^{8} - 11 q^{9} - 11 q^{10} - 11 q^{11} - 11 q^{12} - 11 q^{13} - 11 q^{14} - 385 q^{15} - 451 q^{16} - 99 q^{17} + 77 q^{18} + 99 q^{19} + 693 q^{20} + 649 q^{21} + 462 q^{22} + 473 q^{23} + 1298 q^{24} + 341 q^{25} + 209 q^{26} + 55 q^{27} - 363 q^{28} - 231 q^{29} - 1507 q^{30} - 561 q^{31} - 1507 q^{32} - 979 q^{33} - 1925 q^{34} - 1441 q^{35} - 2486 q^{36} - 1199 q^{37} - 616 q^{38} + 121 q^{39} + 1309 q^{40} + 539 q^{41} + 3619 q^{42} + 1705 q^{43} + 3212 q^{44} + 2948 q^{45} + 3949 q^{46} + 1870 q^{47} + 3333 q^{48} + 2167 q^{49} + 1914 q^{50} + 649 q^{51} + 319 q^{52} - 253 q^{53} - 5511 q^{54} - 4499 q^{55} - 9394 q^{56} - 5951 q^{57} - 7964 q^{58} - 3993 q^{59} - 4081 q^{60} + 517 q^{61} + 1705 q^{62} + 2079 q^{63} + 4213 q^{64} + 4301 q^{65} + 5148 q^{66} + 1441 q^{67} + 8954 q^{68} + 3729 q^{69} + 5786 q^{70} + 3399 q^{71} + 7084 q^{72} + 1045 q^{73} + 968 q^{74} - 5973 q^{75} - 7150 q^{76} - 5467 q^{77} - 11473 q^{78} - 4719 q^{79} - 11110 q^{80} - 6391 q^{81} - 4961 q^{82} - 3861 q^{83} - 5973 q^{84} + 891 q^{85} + 1463 q^{86} + 9361 q^{87} + 6237 q^{88} + 5599 q^{89} + 18502 q^{90} + 7986 q^{91} + 8998 q^{92} + 11726 q^{93} + 8316 q^{94} + 4015 q^{95} + 4092 q^{96} - 2321 q^{97} - 2651 q^{98} - 2321 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(\Gamma_1(23))$$

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 available newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
23.4.a $$\chi_{23}(1, \cdot)$$ 23.4.a.a 1 1
23.4.a.b 4
23.4.c $$\chi_{23}(2, \cdot)$$ 23.4.c.a 50 10