# Properties

 Label 76.7.h Level $76$ Weight $7$ Character orbit 76.h Rep. character $\chi_{76}(65,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $20$ Newform subspaces $1$ Sturm bound $70$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$76 = 2^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$7$$ Character orbit: $$[\chi]$$ $$=$$ 76.h (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$19$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$70$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{7}(76, [\chi])$$.

Total New Old
Modular forms 126 20 106
Cusp forms 114 20 94
Eisenstein series 12 0 12

## Trace form

 $$20q - 30q^{3} - 56q^{5} + 464q^{7} + 2200q^{9} + O(q^{10})$$ $$20q - 30q^{3} - 56q^{5} + 464q^{7} + 2200q^{9} - 3644q^{11} - 7140q^{13} + 9168q^{15} + 1132q^{17} + 2110q^{19} - 8748q^{21} + 832q^{23} - 27698q^{25} - 10920q^{29} - 30306q^{33} + 4172q^{35} + 81144q^{39} + 109206q^{41} + 110740q^{43} - 785440q^{45} + 107080q^{47} + 136092q^{49} + 199872q^{51} + 254796q^{53} + 354840q^{55} + 212268q^{57} - 610638q^{59} + 47864q^{61} - 254476q^{63} - 839562q^{67} + 366660q^{71} + 854482q^{73} + 763088q^{77} + 1718592q^{79} - 1054142q^{81} + 439612q^{83} - 400236q^{85} - 1604736q^{87} + 478032q^{89} + 599856q^{91} + 829380q^{93} - 1055660q^{95} - 191286q^{97} - 2336728q^{99} + O(q^{100})$$

## Decomposition of $$S_{7}^{\mathrm{new}}(76, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
76.7.h.a $$20$$ $$17.484$$ $$\mathbb{Q}[x]/(x^{20} + \cdots)$$ None $$0$$ $$-30$$ $$-56$$ $$464$$ $$q+(-1+\beta _{1}+\beta _{2}-\beta _{3})q^{3}+(-6+6\beta _{3}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{7}^{\mathrm{old}}(76, [\chi])$$ into lower level spaces

$$S_{7}^{\mathrm{old}}(76, [\chi]) \cong$$ $$S_{7}^{\mathrm{new}}(19, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{7}^{\mathrm{new}}(38, [\chi])$$$$^{\oplus 2}$$