# Properties

 Label 315.2.bv Level 315 Weight 2 Character orbit bv Rep. character $$\chi_{315}(23,\cdot)$$ Character field $$\Q(\zeta_{12})$$ Dimension 176 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.bv (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ = $$315$$ Character field: $$\Q(\zeta_{12})$$ 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 208 208 0
Cusp forms 176 176 0
Eisenstein series 32 32 0

## Trace form

 $$176q - 2q^{3} - 6q^{5} - 24q^{6} - 2q^{7} + O(q^{10})$$ $$176q - 2q^{3} - 6q^{5} - 24q^{6} - 2q^{7} - 4q^{10} - 24q^{11} + 26q^{12} - 4q^{13} - 14q^{15} - 136q^{16} + 18q^{17} - 10q^{18} - 12q^{20} - 16q^{21} + 4q^{22} - 30q^{23} + 2q^{25} - 32q^{27} - 4q^{28} + 10q^{30} - 8q^{31} - 34q^{33} + 8q^{36} - 4q^{37} - 30q^{38} + 18q^{40} - 36q^{41} + 8q^{42} - 4q^{43} + 22q^{45} + 4q^{46} + 38q^{48} + 36q^{50} - 40q^{51} + 26q^{52} + 4q^{55} + 24q^{56} + 32q^{57} + 6q^{58} + 22q^{60} + 16q^{61} + 14q^{63} + 4q^{66} - 4q^{67} + 114q^{68} + 18q^{70} - 46q^{72} - 4q^{73} + 6q^{75} - 24q^{76} - 54q^{77} + 54q^{78} - 36q^{80} - 64q^{81} - 8q^{82} - 12q^{83} - 4q^{85} - 120q^{86} - 28q^{87} - 6q^{88} - 24q^{90} - 16q^{91} + 72q^{92} - 38q^{93} + 192q^{96} - 4q^{97} - 12q^{98} + O(q^{100})$$

## 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.bv.a $$176$$ $$2.515$$ None $$0$$ $$-2$$ $$-6$$ $$-2$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database