# Properties

 Label 336.2.bc Level $336$ Weight $2$ Character orbit 336.bc Rep. character $\chi_{336}(17,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $28$ Newform subspaces $6$ 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.bc (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$6$$ Sturm bound: $$128$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$, $$13$$

## Dimensions

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

Total New Old
Modular forms 152 36 116
Cusp forms 104 28 76
Eisenstein series 48 8 40

## Trace form

 $$28 q + 3 q^{3} + 2 q^{7} - q^{9} + O(q^{10})$$ $$28 q + 3 q^{3} + 2 q^{7} - q^{9} - 2 q^{15} + 12 q^{19} - q^{21} - 12 q^{25} + 48 q^{31} - 3 q^{33} - 2 q^{37} + 10 q^{39} - 20 q^{43} - 15 q^{45} - 4 q^{49} - 27 q^{51} - 26 q^{57} - 6 q^{61} - 7 q^{63} + 16 q^{67} - 18 q^{73} - 66 q^{75} - 28 q^{79} + 3 q^{81} + 28 q^{85} - 60 q^{87} - 54 q^{91} + q^{93} + 34 q^{99} + O(q^{100})$$

## 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.bc.a $2$ $2.683$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$-3$$ $$0$$ $$5$$ $$q+(-1-\zeta_{6})q^{3}+(2+\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$$
336.2.bc.b $2$ $2.683$ $$\Q(\sqrt{-3})$$ None $$0$$ $$0$$ $$-3$$ $$-4$$ $$q+(-1+2\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$$
336.2.bc.c $2$ $2.683$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-3})$$ $$0$$ $$3$$ $$0$$ $$-1$$ $$q+(1+\zeta_{6})q^{3}+(-2+3\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots$$
336.2.bc.d $2$ $2.683$ $$\Q(\sqrt{-3})$$ None $$0$$ $$3$$ $$3$$ $$-4$$ $$q+(2-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1-2\zeta_{6})q^{7}+\cdots$$
336.2.bc.e $4$ $2.683$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$10$$ $$q-\zeta_{12}^{2}q^{3}+(-\zeta_{12}^{2}+\zeta_{12}^{3})q^{5}+\cdots$$
336.2.bc.f $16$ $2.683$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+(-\beta _{5}+\beta _{8})q^{3}-\beta _{14}q^{5}+\beta _{10}q^{7}+\cdots$$

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

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