# Properties

 Label 76.3.h Level $76$ Weight $3$ Character orbit 76.h Rep. character $\chi_{76}(65,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $8$ Newform subspaces $1$ Sturm bound $30$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$76 = 2^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$3$$ 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: $$30$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 46 8 38
Cusp forms 34 8 26
Eisenstein series 12 0 12

## Trace form

 $$8 q + 6 q^{3} - q^{5} - 12 q^{7} + 16 q^{9} + O(q^{10})$$ $$8 q + 6 q^{3} - q^{5} - 12 q^{7} + 16 q^{9} - 10 q^{11} + 9 q^{13} + 33 q^{15} + 23 q^{17} - 33 q^{19} - 31 q^{23} - 73 q^{25} - 105 q^{29} - 111 q^{33} - 68 q^{35} + 234 q^{39} + 18 q^{41} - 41 q^{43} + 200 q^{45} + 107 q^{47} + 312 q^{49} - 9 q^{51} + 39 q^{53} + 70 q^{55} - 381 q^{57} + 348 q^{59} - 45 q^{61} - 358 q^{63} - 432 q^{67} - 243 q^{71} + 16 q^{73} + 544 q^{77} + 75 q^{79} - 68 q^{81} - 82 q^{83} + 109 q^{85} + 414 q^{87} - 213 q^{89} + 222 q^{91} + 288 q^{93} - 385 q^{95} + 144 q^{97} - 388 q^{99} + O(q^{100})$$

## 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.h.a $8$ $2.071$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$6$$ $$-1$$ $$-12$$ $$q+(-\beta _{3}-\beta _{4})q^{3}+(\beta _{5}-\beta _{6})q^{5}+(-2+\cdots)q^{7}+\cdots$$

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

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