# Properties

 Label 23.2.c Level 23 Weight 2 Character orbit c Rep. character $$\chi_{23}(2,\cdot)$$ Character field $$\Q(\zeta_{11})$$ Dimension 10 Newforms 1 Sturm bound 4 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$23$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 23.c (of order $$11$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$23$$ Character field: $$\Q(\zeta_{11})$$ Newforms: $$1$$ Sturm bound: $$4$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(23, [\chi])$$.

Total New Old
Modular forms 30 30 0
Cusp forms 10 10 0
Eisenstein series 20 20 0

## Trace form

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

## Decomposition of $$S_{2}^{\mathrm{new}}(23, [\chi])$$ into irreducible Hecke orbits

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
23.2.c.a $$10$$ $$0.184$$ $$\Q(\zeta_{22})$$ None $$-7$$ $$-7$$ $$-3$$ $$-5$$ $$q+(-\zeta_{22}+\zeta_{22}^{4}-\zeta_{22}^{5}+\zeta_{22}^{6}+\cdots)q^{2}+\cdots$$