# Properties

 Label 460.2.g Level $460$ Weight $2$ Character orbit 460.g Rep. character $\chi_{460}(459,\cdot)$ Character field $\Q$ Dimension $68$ Newform subspaces $3$ Sturm bound $144$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$460 = 2^{2} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 460.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$460$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$144$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(460, [\chi])$$.

Total New Old
Modular forms 76 76 0
Cusp forms 68 68 0
Eisenstein series 8 8 0

## Trace form

 $$68q - 8q^{4} - 16q^{6} + 52q^{9} + O(q^{10})$$ $$68q - 8q^{4} - 16q^{6} + 52q^{9} - 8q^{16} - 20q^{24} - 4q^{25} + 24q^{26} - 16q^{29} - 48q^{36} - 16q^{41} + 12q^{46} - 44q^{49} - 32q^{50} - 12q^{54} + 4q^{64} - 28q^{69} - 4q^{70} + 12q^{81} + 16q^{85} + 52q^{94} + 56q^{96} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(460, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
460.2.g.a $$4$$ $$3.673$$ $$\Q(\sqrt{2}, \sqrt{-5})$$ $$\Q(\sqrt{-5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}-\beta _{2}q^{3}+2q^{4}+\beta _{3}q^{5}+2q^{6}+\cdots$$
460.2.g.b $$8$$ $$3.673$$ 8.0.207360000.1 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{2}q^{2}+(\beta _{2}-\beta _{4})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots$$
460.2.g.c $$56$$ $$3.673$$ None $$0$$ $$0$$ $$0$$ $$0$$