Properties

 Label 460.2.c Level $460$ Weight $2$ Character orbit 460.c Rep. character $\chi_{460}(369,\cdot)$ Character field $\Q$ Dimension $12$ 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.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ 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 78 12 66
Cusp forms 66 12 54
Eisenstein series 12 0 12

Trace form

 $$12 q - 20 q^{9} + O(q^{10})$$ $$12 q - 20 q^{9} + 4 q^{11} + 2 q^{15} - 8 q^{19} + 8 q^{25} - 10 q^{29} + 18 q^{31} - 10 q^{35} + 16 q^{39} - 2 q^{41} + 2 q^{45} - 38 q^{49} - 24 q^{51} + 16 q^{55} + 22 q^{59} - 8 q^{61} + 38 q^{65} - 8 q^{69} - 34 q^{71} + 16 q^{75} - 20 q^{79} + 28 q^{81} + 6 q^{85} + 48 q^{89} - 8 q^{91} + 12 q^{95} + 32 q^{99} + O(q^{100})$$

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.c.a $12$ $3.673$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(\beta _{5}+\beta _{6})q^{3}+\beta _{9}q^{5}+(-\beta _{1}-\beta _{6}+\cdots)q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(460, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(115, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(230, [\chi])$$$$^{\oplus 2}$$