# Properties

 Label 96.4.c Level $96$ Weight $4$ Character orbit 96.c Rep. character $\chi_{96}(95,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $1$ Sturm bound $64$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$96 = 2^{5} \cdot 3$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 96.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$12$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$64$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(96, [\chi])$$.

Total New Old
Modular forms 56 12 44
Cusp forms 40 12 28
Eisenstein series 16 0 16

## Trace form

 $$12 q - 20 q^{9} + O(q^{10})$$ $$12 q - 20 q^{9} + 72 q^{13} + 136 q^{21} - 132 q^{25} + 80 q^{33} - 24 q^{37} - 544 q^{45} - 540 q^{49} - 888 q^{57} + 456 q^{61} + 1312 q^{69} + 2424 q^{73} + 2924 q^{81} - 3072 q^{85} - 2360 q^{93} - 2952 q^{97} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(96, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
96.4.c.a $12$ $5.664$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{3}-\beta _{8}q^{5}-\beta _{1}q^{7}+(-2+\beta _{5}+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(96, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(96, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 2}$$