# Properties

 Label 920.2.x Level $920$ Weight $2$ Character orbit 920.x Rep. character $\chi_{920}(413,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $280$ Newform subspaces $3$ Sturm bound $288$ Trace bound $2$

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## Defining parameters

 Level: $$N$$ $$=$$ $$920 = 2^{3} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 920.x (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$920$$ Character field: $$\Q(i)$$ Newform subspaces: $$3$$ Sturm bound: $$288$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(920, [\chi])$$.

Total New Old
Modular forms 296 296 0
Cusp forms 280 280 0
Eisenstein series 16 16 0

## Trace form

 $$280q - 4q^{2} - 16q^{6} - 4q^{8} + O(q^{10})$$ $$280q - 4q^{2} - 16q^{6} - 4q^{8} - 16q^{12} + 16q^{18} - 4q^{23} - 8q^{25} - 8q^{26} + 16q^{31} + 16q^{32} - 8q^{36} - 16q^{41} - 16q^{46} - 8q^{47} - 12q^{48} - 20q^{50} - 96q^{52} - 48q^{55} + 20q^{58} - 68q^{62} + 20q^{70} - 16q^{71} + 16q^{72} - 8q^{73} + 92q^{78} - 264q^{81} - 12q^{82} - 32q^{87} - 20q^{92} + 32q^{95} + 80q^{96} - 52q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(920, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
920.2.x.a $$8$$ $$7.346$$ 8.0.$$\cdots$$.4 $$\Q(\sqrt{-46})$$ $$-8$$ $$0$$ $$0$$ $$0$$ $$q+(-1+\beta _{4})q^{2}-2\beta _{4}q^{4}+\beta _{1}q^{5}+\cdots$$
920.2.x.b $$8$$ $$7.346$$ 8.0.$$\cdots$$.4 $$\Q(\sqrt{-46})$$ $$8$$ $$0$$ $$0$$ $$0$$ $$q+(1-\beta _{3})q^{2}-2\beta _{3}q^{4}-\beta _{4}q^{5}+(-2+\cdots)q^{8}+\cdots$$
920.2.x.c $$264$$ $$7.346$$ None $$-4$$ $$0$$ $$0$$ $$0$$