# Properties

 Label 196.6.e Level $196$ Weight $6$ Character orbit 196.e Rep. character $\chi_{196}(165,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $34$ Newform subspaces $12$ Sturm bound $168$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$196 = 2^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 196.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$12$$ Sturm bound: $$168$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(196, [\chi])$$.

Total New Old
Modular forms 304 34 270
Cusp forms 256 34 222
Eisenstein series 48 0 48

## Trace form

 $$34 q + 9 q^{3} + 61 q^{5} - 1488 q^{9} + O(q^{10})$$ $$34 q + 9 q^{3} + 61 q^{5} - 1488 q^{9} + 291 q^{11} + 724 q^{13} - 4658 q^{15} + 1049 q^{17} + 1767 q^{19} - 6511 q^{23} - 14122 q^{25} - 6822 q^{27} - 12356 q^{29} + 4837 q^{31} + 24439 q^{33} + 3855 q^{37} - 22258 q^{39} - 3876 q^{41} - 71144 q^{43} + 41470 q^{45} + 34299 q^{47} - 60859 q^{51} - 36369 q^{53} - 61414 q^{55} - 80310 q^{57} + 81001 q^{59} + 111625 q^{61} - 31502 q^{65} - 167489 q^{67} - 49706 q^{69} - 161056 q^{71} + 24533 q^{73} + 142172 q^{75} - 86399 q^{79} - 215809 q^{81} + 106712 q^{83} - 599034 q^{85} + 5378 q^{87} + 114405 q^{89} - 213143 q^{93} + 67463 q^{95} - 284740 q^{97} + 576892 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(196, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
196.6.e.a $2$ $31.435$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-26$$ $$-16$$ $$0$$ $$q+(-26+26\zeta_{6})q^{3}-2^{4}\zeta_{6}q^{5}-433\zeta_{6}q^{9}+\cdots$$
196.6.e.b $2$ $31.435$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-19$$ $$19$$ $$0$$ $$q+(-19+19\zeta_{6})q^{3}+19\zeta_{6}q^{5}-118\zeta_{6}q^{9}+\cdots$$
196.6.e.c $2$ $31.435$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-16$$ $$16$$ $$0$$ $$q+(-2^{4}+2^{4}\zeta_{6})q^{3}+2^{4}\zeta_{6}q^{5}-13\zeta_{6}q^{9}+\cdots$$
196.6.e.d $2$ $31.435$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-12$$ $$54$$ $$0$$ $$q+(-12+12\zeta_{6})q^{3}+54\zeta_{6}q^{5}+99\zeta_{6}q^{9}+\cdots$$
196.6.e.e $2$ $31.435$ $$\Q(\sqrt{-3})$$ None $$0$$ $$-2$$ $$-96$$ $$0$$ $$q+(-2+2\zeta_{6})q^{3}-96\zeta_{6}q^{5}+239\zeta_{6}q^{9}+\cdots$$
196.6.e.f $2$ $31.435$ $$\Q(\sqrt{-3})$$ None $$0$$ $$2$$ $$96$$ $$0$$ $$q+(2-2\zeta_{6})q^{3}+96\zeta_{6}q^{5}+239\zeta_{6}q^{9}+\cdots$$
196.6.e.g $2$ $31.435$ $$\Q(\sqrt{-3})$$ None $$0$$ $$12$$ $$-54$$ $$0$$ $$q+(12-12\zeta_{6})q^{3}-54\zeta_{6}q^{5}+99\zeta_{6}q^{9}+\cdots$$
196.6.e.h $2$ $31.435$ $$\Q(\sqrt{-3})$$ None $$0$$ $$16$$ $$-16$$ $$0$$ $$q+(2^{4}-2^{4}\zeta_{6})q^{3}-2^{4}\zeta_{6}q^{5}-13\zeta_{6}q^{9}+\cdots$$
196.6.e.i $2$ $31.435$ $$\Q(\sqrt{-3})$$ None $$0$$ $$26$$ $$16$$ $$0$$ $$q+(26-26\zeta_{6})q^{3}+2^{4}\zeta_{6}q^{5}-433\zeta_{6}q^{9}+\cdots$$
196.6.e.j $4$ $31.435$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+3\beta _{1}q^{3}+(-46\beta _{1}-46\beta _{3})q^{5}-15^{2}\beta _{2}q^{9}+\cdots$$
196.6.e.k $4$ $31.435$ $$\Q(\sqrt{-3}, \sqrt{109})$$ None $$0$$ $$28$$ $$42$$ $$0$$ $$q+(14-14\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(21\beta _{1}+\cdots)q^{5}+\cdots$$
196.6.e.l $8$ $31.435$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{2}-\beta _{5}-\beta _{6})q^{3}+(\beta _{2}+7\beta _{3})q^{5}+\cdots$$

## Decomposition of $$S_{6}^{\mathrm{old}}(196, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(196, [\chi]) \simeq$$ $$S_{6}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(14, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{6}^{\mathrm{new}}(98, [\chi])$$$$^{\oplus 2}$$