# Properties

 Label 525.2.bh Level 525 Weight 2 Character orbit bh Rep. character $$\chi_{525}(13,\cdot)$$ Character field $$\Q(\zeta_{20})$$ Dimension 320 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.bh (of order $$20$$ and degree $$8$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$175$$ Character field: $$\Q(\zeta_{20})$$ 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 672 320 352
Cusp forms 608 320 288
Eisenstein series 64 0 64

## Trace form

 $$320q + 8q^{7} - 24q^{8} + O(q^{10})$$ $$320q + 8q^{7} - 24q^{8} - 8q^{15} + 80q^{16} - 24q^{22} + 36q^{28} - 40q^{29} - 32q^{30} - 48q^{32} + 28q^{35} + 80q^{36} - 32q^{37} + 16q^{42} - 144q^{43} - 288q^{50} + 136q^{53} - 8q^{57} - 32q^{58} - 40q^{60} - 8q^{63} - 120q^{64} - 40q^{65} + 32q^{67} - 40q^{70} - 24q^{72} + 24q^{77} + 8q^{78} + 80q^{81} - 80q^{84} - 48q^{85} - 56q^{88} + 40q^{92} + 96q^{93} - 88q^{95} - 184q^{98} + O(q^{100})$$

## 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.bh.a $$320$$ $$4.192$$ None $$0$$ $$0$$ $$0$$ $$8$$

## Decomposition of $$S_{2}^{\mathrm{old}}(525, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(525, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(175, [\chi])$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database