# Properties

 Label 460.2.w Level $460$ Weight $2$ Character orbit 460.w Rep. character $\chi_{460}(3,\cdot)$ Character field $\Q(\zeta_{44})$ Dimension $1360$ Newform subspaces $1$ Sturm bound $144$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$460 = 2^{2} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 460.w (of order $$44$$ and degree $$20$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$460$$ Character field: $$\Q(\zeta_{44})$$ Newform subspaces: $$1$$ Sturm bound: $$144$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 1520 1520 0
Cusp forms 1360 1360 0
Eisenstein series 160 160 0

## Trace form

 $$1360q - 18q^{2} - 36q^{5} - 44q^{6} - 18q^{8} + O(q^{10})$$ $$1360q - 18q^{2} - 36q^{5} - 44q^{6} - 18q^{8} - 18q^{10} - 6q^{12} - 36q^{13} - 44q^{16} - 36q^{17} - 38q^{18} - 14q^{20} - 88q^{21} - 28q^{22} - 36q^{25} - 36q^{26} - 34q^{28} + 2q^{30} + 2q^{32} - 60q^{33} - 36q^{36} - 36q^{37} - 10q^{38} + 2q^{40} - 56q^{41} - 202q^{42} - 120q^{45} - 44q^{46} - 50q^{48} - 34q^{50} - 250q^{52} - 84q^{53} - 84q^{56} - 44q^{57} - 58q^{58} - 42q^{60} - 136q^{61} - 82q^{62} - 68q^{65} - 84q^{66} - 4q^{68} + 16q^{70} - 104q^{72} - 36q^{73} + 4q^{76} - 44q^{77} - 50q^{78} + 204q^{80} + 80q^{81} - 10q^{82} - 252q^{85} + 44q^{86} - 50q^{88} + 264q^{90} - 22q^{92} - 88q^{93} + 52q^{96} - 36q^{97} + 30q^{98} + O(q^{100})$$

## 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.w.a $$1360$$ $$3.673$$ None $$-18$$ $$0$$ $$-36$$ $$0$$