# Properties

 Label 336.4.h Level $336$ Weight $4$ Character orbit 336.h Rep. character $\chi_{336}(239,\cdot)$ Character field $\Q$ Dimension $36$ Newform subspaces $2$ Sturm bound $256$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$336 = 2^{4} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 336.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$12$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$256$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(336, [\chi])$$.

Total New Old
Modular forms 204 36 168
Cusp forms 180 36 144
Eisenstein series 24 0 24

## Trace form

 $$36 q - 60 q^{9} + O(q^{10})$$ $$36 q - 60 q^{9} - 900 q^{25} - 1152 q^{33} - 1584 q^{37} + 984 q^{45} - 1764 q^{49} - 3456 q^{57} - 1872 q^{61} + 744 q^{69} + 4968 q^{73} - 1836 q^{81} - 7272 q^{85} + 2472 q^{93} + 216 q^{97} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(336, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
336.4.h.a $12$ $19.825$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{5}q^{3}+\beta _{8}q^{5}-\beta _{1}q^{7}+(6-\beta _{2}+\cdots)q^{9}+\cdots$$
336.4.h.b $24$ $19.825$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{4}^{\mathrm{old}}(336, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(336, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{4}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 3}$$