Properties

 Label 460.2.q Level $460$ Weight $2$ Character orbit 460.q Rep. character $\chi_{460}(11,\cdot)$ Character field $\Q(\zeta_{22})$ Dimension $480$ 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.q (of order $$22$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$92$$ Character field: $$\Q(\zeta_{22})$$ 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 760 480 280
Cusp forms 680 480 200
Eisenstein series 80 0 80

Trace form

 $$480 q - 4 q^{2} + 2 q^{6} + 2 q^{8} + 48 q^{9} + O(q^{10})$$ $$480 q - 4 q^{2} + 2 q^{6} + 2 q^{8} + 48 q^{9} + 6 q^{12} - 24 q^{16} + 26 q^{18} + 4 q^{24} + 48 q^{25} - 14 q^{26} + 40 q^{29} + 16 q^{32} - 22 q^{34} - 152 q^{36} - 110 q^{38} - 88 q^{40} - 8 q^{41} - 22 q^{44} - 132 q^{46} - 190 q^{48} - 56 q^{49} - 18 q^{50} - 50 q^{52} - 90 q^{54} - 110 q^{56} - 136 q^{58} - 22 q^{60} + 30 q^{62} - 30 q^{64} + 4 q^{69} + 110 q^{72} + 22 q^{74} - 176 q^{77} + 66 q^{78} - 8 q^{81} + 154 q^{82} + 308 q^{84} + 32 q^{85} + 176 q^{88} - 88 q^{89} + 134 q^{92} - 448 q^{93} + 204 q^{94} + 6 q^{96} - 88 q^{97} + 132 q^{98} + O(q^{100})$$

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.q.a $480$ $3.673$ None $$-4$$ $$0$$ $$0$$ $$0$$

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

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