# Properties

 Label 460.1.n Level $460$ Weight $1$ Character orbit 460.n Rep. character $\chi_{460}(39,\cdot)$ Character field $\Q(\zeta_{22})$ Dimension $20$ Newform subspaces $2$ Sturm bound $72$ Trace bound $2$

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## Defining parameters

 Level: $$N$$ $$=$$ $$460 = 2^{2} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 460.n (of order $$22$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$460$$ Character field: $$\Q(\zeta_{22})$$ Newform subspaces: $$2$$ Sturm bound: $$72$$ Trace bound: $$2$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{1}(460, [\chi])$$.

Total New Old
Modular forms 60 60 0
Cusp forms 20 20 0
Eisenstein series 40 40 0

The following table gives the dimensions of subspaces with specified projective image type.

$$D_n$$ $$A_4$$ $$S_4$$ $$A_5$$
Dimension 20 0 0 0

## Trace form

 $$20 q - 2 q^{4} - 2 q^{5} - 4 q^{6} - 6 q^{9} + O(q^{10})$$ $$20 q - 2 q^{4} - 2 q^{5} - 4 q^{6} - 6 q^{9} - 4 q^{14} - 2 q^{16} - 2 q^{20} - 8 q^{21} - 4 q^{24} - 2 q^{25} - 4 q^{29} - 4 q^{30} - 6 q^{36} - 4 q^{41} + 16 q^{45} - 2 q^{46} + 16 q^{49} + 14 q^{54} + 18 q^{56} - 4 q^{61} - 2 q^{64} - 4 q^{69} - 4 q^{70} - 2 q^{80} - 10 q^{81} + 14 q^{84} + 18 q^{86} - 4 q^{89} - 4 q^{94} - 4 q^{96} + O(q^{100})$$

## Decomposition of $$S_{1}^{\mathrm{new}}(460, [\chi])$$ into newform subspaces

Label Dim $A$ Field Image CM RM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
460.1.n.a $10$ $0.230$ $$\Q(\zeta_{22})$$ $D_{11}$ $$\Q(\sqrt{-5})$$ None $$-1$$ $$-2$$ $$-1$$ $$9$$ $$q+\zeta_{22}^{10}q^{2}+(\zeta_{22}^{2}+\zeta_{22}^{4})q^{3}-\zeta_{22}^{9}q^{4}+\cdots$$
460.1.n.b $10$ $0.230$ $$\Q(\zeta_{22})$$ $D_{11}$ $$\Q(\sqrt{-5})$$ None $$1$$ $$2$$ $$-1$$ $$-9$$ $$q-\zeta_{22}^{10}q^{2}+(-\zeta_{22}^{2}-\zeta_{22}^{4})q^{3}+\cdots$$