# Properties

 Label 460.2.i Level $460$ Weight $2$ Character orbit 460.i Rep. character $\chi_{460}(137,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $24$ 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.i (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$115$$ Character field: $$\Q(i)$$ 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 156 24 132
Cusp forms 132 24 108
Eisenstein series 24 0 24

## Trace form

 $$24 q - 4 q^{3} + O(q^{10})$$ $$24 q - 4 q^{3} + 8 q^{13} - 2 q^{23} + 24 q^{25} + 20 q^{27} - 12 q^{31} - 4 q^{35} - 12 q^{41} + 4 q^{47} + 36 q^{55} + 52 q^{71} - 20 q^{73} - 56 q^{75} - 36 q^{77} - 112 q^{81} - 16 q^{85} - 16 q^{87} + 88 q^{93} - 24 q^{95} + O(q^{100})$$

## 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.i.a $8$ $3.673$ 8.0.$$\cdots$$.3 None $$0$$ $$-8$$ $$0$$ $$0$$ $$q+(-1-\beta _{3})q^{3}+(-\beta _{1}+\beta _{6})q^{5}-\beta _{2}q^{7}+\cdots$$
460.2.i.b $16$ $3.673$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+\beta _{6}q^{3}-\beta _{3}q^{5}+(-\beta _{3}+\beta _{15})q^{7}+\cdots$$

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

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