# Properties

 Label 225.2.q Level 225 Weight 2 Character orbit q Rep. character $$\chi_{225}(16,\cdot)$$ Character field $$\Q(\zeta_{15})$$ Dimension 224 Newform subspaces 1 Sturm bound 60 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$225 = 3^{2} \cdot 5^{2}$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 225.q (of order $$15$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$225$$ Character field: $$\Q(\zeta_{15})$$ Newform subspaces: $$1$$ Sturm bound: $$60$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(225, [\chi])$$.

Total New Old
Modular forms 256 256 0
Cusp forms 224 224 0
Eisenstein series 32 32 0

## Trace form

 $$224q - 3q^{2} - 8q^{3} + 23q^{4} - 8q^{5} - 10q^{6} - 8q^{7} - 20q^{8} - 8q^{9} + O(q^{10})$$ $$224q - 3q^{2} - 8q^{3} + 23q^{4} - 8q^{5} - 10q^{6} - 8q^{7} - 20q^{8} - 8q^{9} - 20q^{10} - 11q^{11} - 4q^{12} - 3q^{13} + q^{14} - 48q^{15} + 23q^{16} - 24q^{17} - 12q^{19} + q^{20} + 15q^{21} - 11q^{22} + q^{23} - 30q^{24} - 16q^{25} - 136q^{26} + 7q^{27} + 4q^{28} - 15q^{29} - 24q^{30} + 3q^{31} + 12q^{32} - 5q^{33} + q^{34} + 14q^{35} + 38q^{36} - 24q^{37} + 55q^{38} + 20q^{39} + q^{40} - 19q^{41} - 38q^{42} - 8q^{43} + 4q^{44} - 38q^{45} - 20q^{46} - 10q^{47} - 25q^{48} - 72q^{49} - 3q^{50} - 26q^{51} - 25q^{52} - 12q^{53} + 53q^{54} - 20q^{55} - 60q^{56} + 38q^{57} - 23q^{58} - 30q^{59} - 33q^{60} - 3q^{61} - 44q^{62} + 46q^{63} - 44q^{64} + 51q^{65} - 134q^{66} - 12q^{67} - 156q^{68} + 4q^{69} - 16q^{70} + 42q^{71} + 74q^{72} - 12q^{73} + 90q^{74} + 67q^{75} - 8q^{76} + 31q^{77} - 92q^{78} - 15q^{79} + 298q^{80} - 104q^{81} + 8q^{82} + 59q^{83} + 115q^{84} - 11q^{85} + 9q^{86} - 59q^{87} - 23q^{88} + 106q^{89} + 107q^{90} + 30q^{91} + 11q^{92} + 32q^{93} + 25q^{94} + 7q^{95} + 35q^{96} - 21q^{97} + 146q^{98} - 20q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(225, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
225.2.q.a $$224$$ $$1.797$$ None $$-3$$ $$-8$$ $$-8$$ $$-8$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database