# Properties

 Label 525.2.bm Level 525 Weight 2 Character orbit bm Rep. character $$\chi_{525}(131,\cdot)$$ Character field $$\Q(\zeta_{30})$$ Dimension 608 Newform subspaces 1 Sturm bound 160 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$525 = 3 \cdot 5^{2} \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 525.bm (of order $$30$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$525$$ Character field: $$\Q(\zeta_{30})$$ Newform subspaces: $$1$$ Sturm bound: $$160$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(525, [\chi])$$.

Total New Old
Modular forms 672 672 0
Cusp forms 608 608 0
Eisenstein series 64 64 0

## Trace form

 $$608q - 9q^{3} - 78q^{4} - 36q^{7} - 3q^{9} + O(q^{10})$$ $$608q - 9q^{3} - 78q^{4} - 36q^{7} - 3q^{9} - 30q^{10} + 3q^{12} + 16q^{15} + 50q^{16} - 8q^{18} - 18q^{19} - 21q^{21} - 24q^{22} - 66q^{24} - 10q^{25} - 30q^{28} - 7q^{30} - 36q^{31} + 36q^{33} - 100q^{36} - 14q^{37} - 31q^{39} - 30q^{40} + 20q^{42} - 96q^{43} - 117q^{45} + 42q^{46} - 28q^{49} - 8q^{51} - 66q^{52} + 3q^{54} + 48q^{57} - 38q^{58} - 49q^{60} - 18q^{61} + 4q^{63} - 32q^{64} - 3q^{66} - 22q^{67} - 270q^{70} + 45q^{72} + 102q^{73} + 135q^{75} + 58q^{78} - 34q^{79} - 55q^{81} + 108q^{82} - 75q^{84} - 96q^{85} - 9q^{87} + 36q^{88} + 38q^{91} - 22q^{93} + 30q^{94} - 81q^{96} + 36q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(525, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
525.2.bm.a $$608$$ $$4.192$$ None $$0$$ $$-9$$ $$0$$ $$-36$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database