# Properties

 Label 76.5.c Level $76$ Weight $5$ Character orbit 76.c Rep. character $\chi_{76}(37,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $2$ Sturm bound $50$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$76 = 2^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$5$$ Character orbit: $$[\chi]$$ $$=$$ 76.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$50$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{5}(76, [\chi])$$.

Total New Old
Modular forms 43 6 37
Cusp forms 37 6 31
Eisenstein series 6 0 6

## Trace form

 $$6q - 9q^{5} + 97q^{7} - 52q^{9} + O(q^{10})$$ $$6q - 9q^{5} + 97q^{7} - 52q^{9} + 39q^{11} - 723q^{17} + 68q^{19} + 774q^{23} + 1153q^{25} - 861q^{35} - 2262q^{39} + 579q^{43} - 5681q^{45} + 4047q^{47} + 2787q^{49} - 6533q^{55} + 5490q^{57} + 2911q^{61} + 643q^{63} + 177q^{73} + 17739q^{77} - 17014q^{81} - 7488q^{83} - 401q^{85} - 14526q^{87} - 1284q^{93} - 837q^{95} + 27259q^{99} + O(q^{100})$$

## Decomposition of $$S_{5}^{\mathrm{new}}(76, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
76.5.c.a $$2$$ $$7.856$$ $$\Q(\sqrt{57})$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$-31$$ $$73$$ $$q+(-17-3\beta )q^{5}+(39+5\beta )q^{7}+3^{4}q^{9}+\cdots$$
76.5.c.b $$4$$ $$7.856$$ $$\mathbb{Q}[x]/(x^{4} + \cdots)$$ None $$0$$ $$0$$ $$22$$ $$24$$ $$q+\beta _{1}q^{3}+(6-\beta _{2})q^{5}+(7-2\beta _{2})q^{7}+\cdots$$

## Decomposition of $$S_{5}^{\mathrm{old}}(76, [\chi])$$ into lower level spaces

$$S_{5}^{\mathrm{old}}(76, [\chi]) \cong$$ $$S_{5}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{5}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 2}$$