# Properties

 Label 336.2.q Level $336$ Weight $2$ Character orbit 336.q Rep. character $\chi_{336}(193,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $16$ Newform subspaces $7$ Sturm bound $128$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$336 = 2^{4} \cdot 3 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 336.q (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$7$$ Sturm bound: $$128$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(336, [\chi])$$.

Total New Old
Modular forms 152 16 136
Cusp forms 104 16 88
Eisenstein series 48 0 48

## Trace form

 $$16 q - 2 q^{3} - 2 q^{7} - 8 q^{9} + O(q^{10})$$ $$16 q - 2 q^{3} - 2 q^{7} - 8 q^{9} + 4 q^{11} - 10 q^{19} + 16 q^{23} - 12 q^{25} + 4 q^{27} + 16 q^{29} + 14 q^{31} - 4 q^{33} + 36 q^{35} - 8 q^{37} + 2 q^{39} + 16 q^{41} - 12 q^{43} - 12 q^{47} - 16 q^{49} - 16 q^{53} - 56 q^{55} - 8 q^{57} - 16 q^{59} - 8 q^{61} - 2 q^{63} - 8 q^{65} - 6 q^{67} + 24 q^{71} + 12 q^{73} - 14 q^{75} + 8 q^{77} + 18 q^{79} - 8 q^{81} - 24 q^{83} - 16 q^{85} + 12 q^{87} + 16 q^{89} + 54 q^{91} + 8 q^{93} - 36 q^{95} + 8 q^{97} - 8 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(336, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
336.2.q.a $2$ $2.683$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-2$$ $$-5$$ $$q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+\cdots$$
336.2.q.b $2$ $2.683$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$-1$$ $$-1$$ $$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots$$
336.2.q.c $2$ $2.683$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-1$$ $$2$$ $$-1$$ $$q+(-1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(-2+3\zeta_{6})q^{7}+\cdots$$
336.2.q.d $2$ $2.683$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$-3$$ $$-5$$ $$q+(1-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-3+\zeta_{6})q^{7}+\cdots$$
336.2.q.e $2$ $2.683$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$1$$ $$-1$$ $$q+(1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots$$
336.2.q.f $2$ $2.683$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$2$$ $$5$$ $$q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(2+\zeta_{6})q^{7}+\cdots$$
336.2.q.g $4$ $2.683$ $$\Q(\sqrt{-3}, \sqrt{-19})$$ None $$0$$ $$-2$$ $$1$$ $$6$$ $$q+(-1+\beta _{2})q^{3}+(-1+2\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(336, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(336, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(56, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(84, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(112, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(168, [\chi])$$$$^{\oplus 2}$$