# Properties

 Label 770.2.bv Level $770$ Weight $2$ Character orbit 770.bv Rep. character $\chi_{770}(3,\cdot)$ Character field $\Q(\zeta_{60})$ Dimension $768$ Newform subspaces $1$ Sturm bound $288$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$770 = 2 \cdot 5 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 770.bv (of order $$60$$ and degree $$16$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$385$$ Character field: $$\Q(\zeta_{60})$$ Newform subspaces: $$1$$ Sturm bound: $$288$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(770, [\chi])$$.

Total New Old
Modular forms 2432 768 1664
Cusp forms 2176 768 1408
Eisenstein series 256 0 256

## Trace form

 $$768 q + 24 q^{5} + 4 q^{7} + O(q^{10})$$ $$768 q + 24 q^{5} + 4 q^{7} + 24 q^{10} + 12 q^{11} - 24 q^{15} - 96 q^{16} + 8 q^{22} + 8 q^{23} + 16 q^{25} - 24 q^{26} - 28 q^{28} - 16 q^{30} + 252 q^{33} - 40 q^{35} + 160 q^{36} - 8 q^{37} - 44 q^{42} + 80 q^{43} + 96 q^{45} - 8 q^{46} - 24 q^{47} + 64 q^{50} - 8 q^{51} + 40 q^{53} + 16 q^{56} + 64 q^{57} - 48 q^{58} - 164 q^{63} - 88 q^{65} + 32 q^{67} - 100 q^{70} + 32 q^{71} + 120 q^{73} - 336 q^{75} - 96 q^{77} - 36 q^{80} - 24 q^{81} + 48 q^{82} - 112 q^{85} - 24 q^{87} + 4 q^{88} - 12 q^{91} - 16 q^{92} - 88 q^{93} - 44 q^{95} + 32 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(770, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
770.2.bv.a $768$ $6.148$ None $$0$$ $$0$$ $$24$$ $$4$$

## Decomposition of $$S_{2}^{\mathrm{old}}(770, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(770, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(385, [\chi])$$$$^{\oplus 2}$$