# Properties

 Label 225.2.u Level 225 Weight 2 Character orbit u Rep. character $$\chi_{225}(4,\cdot)$$ Character field $$\Q(\zeta_{30})$$ 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.u (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$225$$ Character field: $$\Q(\zeta_{30})$$ 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

 $$224q - 5q^{2} - 10q^{3} - 29q^{4} - 2q^{6} - 20q^{8} - 8q^{9} + O(q^{10})$$ $$224q - 5q^{2} - 10q^{3} - 29q^{4} - 2q^{6} - 20q^{8} - 8q^{9} - 12q^{10} + 5q^{11} - 30q^{12} - 5q^{13} - 23q^{14} + 18q^{15} + 15q^{16} - 20q^{17} - 12q^{19} - 17q^{20} - 27q^{21} - 5q^{22} - 5q^{23} - 46q^{24} - 16q^{25} + 72q^{26} - 25q^{27} - 60q^{28} - 15q^{29} + 2q^{30} - 9q^{31} - 35q^{33} - 7q^{34} - 46q^{35} - 66q^{36} - 20q^{37} - 75q^{38} + 32q^{39} - q^{40} + 13q^{41} - 140q^{42} + 20q^{44} + 90q^{45} - 4q^{46} + 20q^{47} + 165q^{48} + 56q^{49} - 29q^{50} - 6q^{51} - 15q^{52} - 20q^{53} + 61q^{54} - 44q^{55} + 22q^{56} - 5q^{58} - 30q^{59} - 149q^{60} - 3q^{61} + 40q^{62} - 12q^{64} + 45q^{65} + 98q^{66} + 10q^{67} - 14q^{69} - 12q^{70} - 106q^{71} + 40q^{72} - 20q^{73} + 82q^{74} + 43q^{75} + 8q^{76} - 115q^{77} + 110q^{78} - 15q^{79} - 22q^{80} + 72q^{81} + 65q^{83} + 57q^{84} - 21q^{85} - 15q^{86} + 115q^{87} - 5q^{88} + 26q^{89} - 29q^{90} - 54q^{91} + 95q^{92} + 41q^{94} - 17q^{95} - 47q^{96} - 5q^{97} - 70q^{98} + O(q^{100})$$

## 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.u.a $$224$$ $$1.797$$ None $$-5$$ $$-10$$ $$0$$ $$0$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database