# Properties

 Label 196.2.f Level $196$ Weight $2$ Character orbit 196.f Rep. character $\chi_{196}(19,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $32$ Newform subspaces $4$ Sturm bound $56$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$196 = 2^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 196.f (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$28$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$56$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$, $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(196, [\chi])$$.

Total New Old
Modular forms 72 48 24
Cusp forms 40 32 8
Eisenstein series 32 16 16

## Trace form

 $$32 q + 3 q^{2} - q^{4} + 6 q^{5} - 6 q^{8} - 6 q^{9} + O(q^{10})$$ $$32 q + 3 q^{2} - q^{4} + 6 q^{5} - 6 q^{8} - 6 q^{9} - 6 q^{10} - 12 q^{12} - 13 q^{16} + 6 q^{17} + 17 q^{18} + 12 q^{24} - 2 q^{25} + 12 q^{26} - 56 q^{29} + 34 q^{30} - 17 q^{32} - 6 q^{33} - 22 q^{36} + 14 q^{37} - 18 q^{38} - 12 q^{40} - 34 q^{44} - 8 q^{46} - 26 q^{50} - 10 q^{53} + 18 q^{54} + 28 q^{57} + 14 q^{58} - 20 q^{60} + 18 q^{61} - 22 q^{64} - 20 q^{65} + 6 q^{66} + 19 q^{72} - 30 q^{73} + 24 q^{74} + 40 q^{78} + 24 q^{80} + 20 q^{81} - 12 q^{82} - 52 q^{85} - 54 q^{86} + 54 q^{88} - 54 q^{89} + 92 q^{92} + 38 q^{93} + 30 q^{94} + 24 q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(196, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
196.2.f.a $4$ $1.565$ $$\Q(\zeta_{12})$$ None $$-2$$ $$0$$ $$6$$ $$0$$ $$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots$$
196.2.f.b $4$ $1.565$ $$\Q(\sqrt{-3}, \sqrt{-7})$$ $$\Q(\sqrt{-7})$$ $$1$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{2}+(1+\beta _{1}-\beta _{2})q^{4}+(3-\beta _{1}+\cdots)q^{8}+\cdots$$
196.2.f.c $8$ $1.565$ 8.0.339738624.1 $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{2}-\beta _{5})q^{2}+2\beta _{4}q^{4}-\beta _{3}q^{5}+\cdots$$
196.2.f.d $16$ $1.565$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$4$$ $$0$$ $$0$$ $$0$$ $$q+(-\beta _{6}-\beta _{11})q^{2}+(2\beta _{1}+\beta _{3})q^{3}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(196, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(196, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 2}$$