# Properties

 Label 49.2.c Level $49$ Weight $2$ Character orbit 49.c Rep. character $\chi_{49}(18,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $2$ Newform subspaces $1$ Sturm bound $9$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$49 = 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 49.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$1$$ Sturm bound: $$9$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(49, [\chi])$$.

Total New Old
Modular forms 18 10 8
Cusp forms 2 2 0
Eisenstein series 16 8 8

## Trace form

 $$2 q - q^{2} + q^{4} - 6 q^{8} + 3 q^{9} + O(q^{10})$$ $$2 q - q^{2} + q^{4} - 6 q^{8} + 3 q^{9} - 4 q^{11} + q^{16} + 3 q^{18} + 8 q^{22} - 8 q^{23} + 5 q^{25} + 4 q^{29} - 5 q^{32} + 6 q^{36} + 6 q^{37} - 24 q^{43} + 4 q^{44} - 8 q^{46} - 10 q^{50} + 10 q^{53} - 2 q^{58} + 14 q^{64} - 4 q^{67} + 32 q^{71} - 9 q^{72} + 6 q^{74} - 8 q^{79} - 9 q^{81} + 12 q^{86} + 12 q^{88} - 16 q^{92} - 24 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(49, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
49.2.c.a $2$ $0.391$ $$\Q(\sqrt{-3})$$ $$\Q(\sqrt{-7})$$ $$-1$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-3q^{8}+3\zeta_{6}q^{9}+\cdots$$