# Properties

 Label 76.2.d Level $76$ Weight $2$ Character orbit 76.d Rep. character $\chi_{76}(75,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $1$ Sturm bound $20$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$76 = 2^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 76.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$76$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$20$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(76, [\chi])$$.

Total New Old
Modular forms 12 12 0
Cusp forms 8 8 0
Eisenstein series 4 4 0

## Trace form

 $$8 q - 6 q^{4} - 4 q^{5} - 2 q^{6} + 4 q^{9} + O(q^{10})$$ $$8 q - 6 q^{4} - 4 q^{5} - 2 q^{6} + 4 q^{9} - 6 q^{16} - 8 q^{17} + 20 q^{20} - 10 q^{24} - 4 q^{25} - 6 q^{26} + 22 q^{28} - 16 q^{30} - 20 q^{36} + 18 q^{38} + 50 q^{42} + 16 q^{44} - 36 q^{45} - 16 q^{49} + 22 q^{54} + 20 q^{57} - 38 q^{58} + 44 q^{61} - 20 q^{62} - 18 q^{64} - 44 q^{66} + 6 q^{68} + 32 q^{73} + 44 q^{74} - 16 q^{76} + 28 q^{77} - 48 q^{80} - 48 q^{81} - 44 q^{82} + 4 q^{85} - 38 q^{92} + 8 q^{93} + 74 q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(76, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
76.2.d.a $8$ $0.607$ 8.0.$$\cdots$$.1 None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots$$