# Properties

 Label 68.2.h Level $68$ Weight $2$ Character orbit 68.h Rep. character $\chi_{68}(9,\cdot)$ Character field $\Q(\zeta_{8})$ 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.h (of order $$8$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$17$$ Character field: $$\Q(\zeta_{8})$$ 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 48 4 44
Cusp forms 24 4 20
Eisenstein series 24 0 24

## Trace form

 $$4 q + 4 q^{5} - 4 q^{9} + O(q^{10})$$ $$4 q + 4 q^{5} - 4 q^{9} - 8 q^{11} - 4 q^{15} - 12 q^{17} - 4 q^{19} + 8 q^{23} + 4 q^{25} - 12 q^{27} + 12 q^{29} + 24 q^{31} + 8 q^{33} + 4 q^{37} + 24 q^{39} + 4 q^{41} - 12 q^{43} - 4 q^{45} - 4 q^{49} - 8 q^{51} - 28 q^{53} - 4 q^{57} - 28 q^{59} + 4 q^{61} + 4 q^{63} + 8 q^{65} - 24 q^{69} + 16 q^{71} - 12 q^{73} + 8 q^{75} - 4 q^{77} - 8 q^{79} + 12 q^{83} - 20 q^{85} - 4 q^{87} + 8 q^{91} + 28 q^{93} + 12 q^{95} + 12 q^{97} + 12 q^{99} + O(q^{100})$$

## 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.h.a $4$ $0.543$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(1-\zeta_{8})q^{5}+(\zeta_{8}+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(68, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(17, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(34, [\chi])$$$$^{\oplus 2}$$