Properties

 Label 68.2.b Level $68$ Weight $2$ Character orbit 68.b Rep. character $\chi_{68}(33,\cdot)$ Character field $\Q$ Dimension $2$ 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.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$17$$ Character field: $$\Q$$ 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 12 2 10
Cusp forms 6 2 4
Eisenstein series 6 0 6

Trace form

 $$2 q + 2 q^{9} + O(q^{10})$$ $$2 q + 2 q^{9} - 8 q^{13} - 8 q^{15} + 6 q^{17} - 8 q^{19} + 12 q^{21} - 6 q^{25} + 4 q^{33} + 24 q^{35} + 16 q^{43} - 24 q^{47} - 22 q^{49} + 8 q^{51} - 12 q^{53} + 8 q^{55} - 8 q^{67} + 4 q^{69} - 12 q^{77} - 10 q^{81} + 16 q^{85} - 8 q^{87} + 24 q^{89} - 12 q^{93} + O(q^{100})$$

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.b.a $2$ $0.543$ $$\Q(\sqrt{-2})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{3}+2\beta q^{5}-3\beta q^{7}+q^{9}-\beta q^{11}+\cdots$$

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

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