# Properties

 Label 196.2.e Level $196$ Weight $2$ Character orbit 196.e Rep. character $\chi_{196}(165,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $6$ Newform subspaces $2$ Sturm bound $56$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$196 = 2^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 196.e (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$2$$ Sturm bound: $$56$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 80 6 74
Cusp forms 32 6 26
Eisenstein series 48 0 48

## Trace form

 $$6q + q^{3} + 3q^{5} - 8q^{9} + O(q^{10})$$ $$6q + q^{3} + 3q^{5} - 8q^{9} - 5q^{11} - 4q^{13} - 10q^{15} + 3q^{17} - q^{19} + 5q^{23} + 2q^{25} + 10q^{27} + 20q^{29} - 7q^{31} - 3q^{33} + 17q^{37} + 22q^{39} - 12q^{41} - 24q^{43} - 6q^{45} - 9q^{47} + 5q^{51} - 23q^{53} + 18q^{55} - 34q^{57} + 9q^{59} - q^{61} - 18q^{65} + 7q^{67} - 6q^{69} - q^{73} + 4q^{75} - 3q^{79} - 3q^{81} - 24q^{83} + 26q^{85} - 6q^{87} + 15q^{89} + 7q^{93} - 5q^{95} + 20q^{97} + 92q^{99} + O(q^{100})$$

## 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.e.a $$2$$ $$1.565$$ $$\Q(\sqrt{-3})$$ None $$0$$ $$1$$ $$3$$ $$0$$ $$q+(1-\zeta_{6})q^{3}+3\zeta_{6}q^{5}+2\zeta_{6}q^{9}+(3+\cdots)q^{11}+\cdots$$
196.2.e.b $$4$$ $$1.565$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\beta _{1}q^{3}+(\beta _{1}+\beta _{3})q^{5}+5\beta _{2}q^{9}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(196, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(28, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(49, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(98, [\chi])$$$$^{\oplus 2}$$