# Properties

 Label 76.3.c Level $76$ Weight $3$ Character orbit 76.c Rep. character $\chi_{76}(37,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $2$ Sturm bound $30$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$76 = 2^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ 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: $$30$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(76, [\chi])$$.

Total New Old
Modular forms 23 4 19
Cusp forms 17 4 13
Eisenstein series 6 0 6

## Trace form

 $$4 q + q^{5} + 3 q^{7} - 22 q^{9} + O(q^{10})$$ $$4 q + q^{5} + 3 q^{7} - 22 q^{9} + 25 q^{11} + 31 q^{17} - 18 q^{19} - 62 q^{23} + q^{25} - 55 q^{35} - 174 q^{39} + 221 q^{43} + 241 q^{45} - 23 q^{47} + 75 q^{49} + 17 q^{55} - 174 q^{57} - 183 q^{61} + 85 q^{63} + 11 q^{73} - 463 q^{77} + 440 q^{81} + 244 q^{83} - 451 q^{85} + 522 q^{87} + 348 q^{93} - 251 q^{95} - 587 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(76, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
76.3.c.a $2$ $2.071$ $$\Q(\sqrt{-29})$$ None $$0$$ $$0$$ $$-8$$ $$-2$$ $$q+\beta q^{3}-4q^{5}-q^{7}-20q^{9}+14q^{11}+\cdots$$
76.3.c.b $2$ $2.071$ $$\Q(\sqrt{57})$$ $$\Q(\sqrt{-19})$$ $$0$$ $$0$$ $$9$$ $$5$$ $$q+(5-\beta )q^{5}+(1+3\beta )q^{7}+9q^{9}+(1+\cdots)q^{11}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(76, [\chi])$$ into lower level spaces

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