# Properties

 Label 315.2.bq Level 315 Weight 2 Character orbit bq Rep. character $$\chi_{315}(164,\cdot)$$ Character field $$\Q(\zeta_{6})$$ Dimension 88 Newform subspaces 1 Sturm bound 96 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ = $$315 = 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 315.bq (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$315$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$96$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(315, [\chi])$$.

Total New Old
Modular forms 104 104 0
Cusp forms 88 88 0
Eisenstein series 16 16 0

## Trace form

 $$88q + 76q^{4} - 3q^{5} - 12q^{6} + O(q^{10})$$ $$88q + 76q^{4} - 3q^{5} - 12q^{6} - 6q^{10} - 12q^{11} - 12q^{14} - 6q^{15} + 52q^{16} - 12q^{19} - 6q^{20} - 12q^{21} - 48q^{24} + q^{25} - 12q^{26} + 6q^{29} + 33q^{30} - 12q^{34} - 36q^{36} + 12q^{39} - 30q^{40} + 6q^{41} - 84q^{44} + 21q^{45} - 18q^{46} - 8q^{49} + 30q^{50} - 24q^{51} - 60q^{54} - 78q^{56} - 12q^{59} - 45q^{60} - 8q^{64} - 24q^{66} + 60q^{69} + 15q^{70} - 30q^{74} - 48q^{75} - 48q^{76} - 16q^{79} - 69q^{80} + 36q^{81} - 90q^{84} - 7q^{85} - 12q^{86} + 72q^{89} + 33q^{90} + 20q^{91} - 60q^{96} + 30q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(315, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
315.2.bq.a $$88$$ $$2.515$$ None $$0$$ $$0$$ $$-3$$ $$0$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database