# Properties

 Label 68.2.e Level $68$ Weight $2$ Character orbit 68.e Rep. character $\chi_{68}(13,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $4$ Newform subspaces $1$ Sturm bound $18$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$68 = 2^{2} \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 68.e (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$17$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$18$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(68, [\chi])$$.

Total New Old
Modular forms 24 4 20
Cusp forms 12 4 8
Eisenstein series 12 0 12

## Trace form

 $$4 q - 2 q^{3} - 4 q^{5} + 2 q^{7} + O(q^{10})$$ $$4 q - 2 q^{3} - 4 q^{5} + 2 q^{7} + 6 q^{11} - 4 q^{13} - 28 q^{21} - 10 q^{23} + 28 q^{27} + 8 q^{29} + 10 q^{31} + 20 q^{33} - 4 q^{35} + 12 q^{37} - 24 q^{39} + 4 q^{41} + 16 q^{45} - 16 q^{47} - 30 q^{51} - 12 q^{55} - 20 q^{57} + 4 q^{61} + 34 q^{63} + 4 q^{65} + 8 q^{67} + 36 q^{69} - 10 q^{71} - 28 q^{73} - 6 q^{75} + 6 q^{79} - 32 q^{81} - 8 q^{85} - 12 q^{89} + 24 q^{91} + 12 q^{95} - 16 q^{97} - 2 q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(68, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
68.2.e.a $4$ $0.543$ $$\Q(i, \sqrt{13})$$ None $$0$$ $$-2$$ $$-4$$ $$2$$ $$q+(-1+\beta _{2})q^{3}+(-1-\beta _{1})q^{5}+(1+\cdots)q^{7}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(68, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(68, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(34, [\chi])$$$$^{\oplus 2}$$