# Properties

 Label 460.2.e Level $460$ Weight $2$ Character orbit 460.e Rep. character $\chi_{460}(91,\cdot)$ Character field $\Q$ Dimension $48$ Newform subspaces $2$ 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.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$92$$ Character field: $$\Q$$ Newform subspaces: $$2$$ 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 48 28
Cusp forms 68 48 20
Eisenstein series 8 0 8

## Trace form

 $$48q + 4q^{2} - 2q^{6} - 2q^{8} - 48q^{9} + O(q^{10})$$ $$48q + 4q^{2} - 2q^{6} - 2q^{8} - 48q^{9} - 6q^{12} + 24q^{16} - 26q^{18} - 4q^{24} - 48q^{25} + 14q^{26} - 40q^{29} - 16q^{32} + 42q^{36} + 8q^{41} - 44q^{46} + 14q^{48} + 56q^{49} - 4q^{50} + 50q^{52} + 2q^{54} + 26q^{58} - 30q^{62} + 30q^{64} - 4q^{69} - 110q^{72} + 154q^{78} + 8q^{81} - 22q^{82} - 32q^{85} + 64q^{92} - 80q^{93} - 6q^{94} - 6q^{96} + 44q^{98} + O(q^{100})$$

## 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.e.a $$16$$ $$3.673$$ 16.0.$$\cdots$$.3 None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{4}q^{2}+\beta _{8}q^{3}+(-\beta _{2}+\beta _{8})q^{4}+\cdots$$
460.2.e.b $$32$$ $$3.673$$ None $$4$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(460, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(460, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(92, [\chi])$$$$^{\oplus 2}$$