# Properties

 Label 920.2.b Level $920$ Weight $2$ Character orbit 920.b Rep. character $\chi_{920}(459,\cdot)$ Character field $\Q$ Dimension $140$ Newform subspaces $2$ Sturm bound $288$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$920 = 2^{3} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 920.b (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$920$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$288$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

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

Total New Old
Modular forms 148 148 0
Cusp forms 140 140 0
Eisenstein series 8 8 0

## Trace form

 $$140q + 8q^{6} - 140q^{9} + O(q^{10})$$ $$140q + 8q^{6} - 140q^{9} - 8q^{16} + 4q^{24} - 4q^{25} + 8q^{26} + 16q^{35} - 24q^{36} - 8q^{41} - 8q^{46} - 124q^{49} + 4q^{50} - 76q^{54} - 8q^{59} + 36q^{64} - 8q^{70} + 8q^{75} + 108q^{81} + 44q^{94} + 16q^{96} + O(q^{100})$$

## 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.b.a $$4$$ $$7.346$$ $$\Q(\sqrt{2}, \sqrt{-5})$$ $$\Q(\sqrt{-10})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{2}+2q^{4}-\beta _{3}q^{5}-2\beta _{3}q^{7}+\cdots$$
920.2.b.b $$136$$ $$7.346$$ None $$0$$ $$0$$ $$0$$ $$0$$