# Properties

 Label 196.2.d Level $196$ Weight $2$ Character orbit 196.d Rep. character $\chi_{196}(195,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $3$ 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.d (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$28$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$56$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 36 24 12
Cusp forms 20 16 4
Eisenstein series 16 8 8

## Trace form

 $$16q + 4q^{4} - 12q^{8} + 12q^{9} + O(q^{10})$$ $$16q + 4q^{4} - 12q^{8} + 12q^{9} + 4q^{16} - 20q^{18} + 12q^{22} - 4q^{25} - 16q^{29} - 28q^{30} + 20q^{32} - 20q^{36} - 20q^{37} + 16q^{44} - 4q^{46} - 4q^{50} + 28q^{53} - 4q^{57} - 8q^{58} + 32q^{60} - 20q^{64} + 8q^{65} - 4q^{72} - 12q^{74} + 32q^{78} - 56q^{81} - 20q^{85} + 72q^{86} - 72q^{88} + 64q^{92} - 44q^{93} + O(q^{100})$$

## 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.d.a $$4$$ $$1.565$$ 4.0.2048.2 $$\Q(\sqrt{-1})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+2q^{4}+\beta _{1}q^{5}-2\beta _{2}q^{8}+\cdots$$
196.2.d.b $$4$$ $$1.565$$ $$\Q(\zeta_{12})$$ None $$4$$ $$0$$ $$0$$ $$0$$ $$q+(1+\zeta_{12})q^{2}+\zeta_{12}^{3}q^{3}+2\zeta_{12}q^{4}+\cdots$$
196.2.d.c $$8$$ $$1.565$$ 8.0.$$\cdots$$.10 None $$-4$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\beta _{5})q^{2}+(-2\beta _{1}-\beta _{7})q^{3}+\cdots$$

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

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