# Properties

 Label 525.2.bp Level 525 Weight 2 Character orbit bp Rep. character $$\chi_{525}(59,\cdot)$$ 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.bp (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

 $$608q - 15q^{3} + 66q^{4} - 3q^{9} + O(q^{10})$$ $$608q - 15q^{3} + 66q^{4} - 3q^{9} - 30q^{10} - 15q^{12} - 36q^{15} + 66q^{16} - 18q^{19} + 9q^{21} - 80q^{22} - 30q^{24} + 2q^{25} - 90q^{28} - 23q^{30} - 90q^{33} + 44q^{36} - 10q^{37} - 19q^{39} + 42q^{40} - 70q^{42} - 117q^{45} - 54q^{46} - 28q^{49} - 8q^{51} - 30q^{52} - 21q^{54} + 50q^{58} - 67q^{60} - 18q^{61} - 70q^{63} - 176q^{64} + 57q^{66} - 10q^{67} + 42q^{70} - 45q^{72} - 150q^{73} + 33q^{75} + 10q^{78} - 34q^{79} + 49q^{81} - 53q^{84} - 8q^{85} - 15q^{87} + 80q^{88} - 62q^{91} + 30q^{94} - 9q^{96} + 36q^{99} + O(q^{100})$$

## 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.bp.a $$608$$ $$4.192$$ None $$0$$ $$-15$$ $$0$$ $$0$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database