# Properties

 Label 240.2.v Level $240$ Weight $2$ Character orbit 240.v Rep. character $\chi_{240}(17,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $20$ Newform subspaces $5$ Sturm bound $96$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$240 = 2^{4} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 240.v (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q(i)$$ Newform subspaces: $$5$$ Sturm bound: $$96$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$17$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(240, [\chi])$$.

Total New Old
Modular forms 120 28 92
Cusp forms 72 20 52
Eisenstein series 48 8 40

## Trace form

 $$20 q + 2 q^{3} + 4 q^{7} + O(q^{10})$$ $$20 q + 2 q^{3} + 4 q^{7} - 4 q^{13} + 14 q^{15} - 12 q^{21} - 4 q^{25} + 14 q^{27} + 4 q^{33} - 20 q^{37} - 12 q^{43} - 12 q^{45} - 20 q^{51} - 40 q^{55} + 20 q^{57} - 24 q^{61} - 48 q^{63} - 20 q^{67} + 4 q^{73} - 38 q^{75} + 4 q^{81} - 20 q^{85} - 20 q^{87} + 56 q^{91} - 8 q^{93} + 4 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(240, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
240.2.v.a $4$ $1.916$ $$\Q(\zeta_{8})$$ None $$0$$ $$-4$$ $$4$$ $$4$$ $$q+(-1+\zeta_{8}^{2})q^{3}+(1+2\zeta_{8})q^{5}+(1+\cdots)q^{7}+\cdots$$
240.2.v.b $4$ $1.916$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$-2$$ $$0$$ $$4$$ $$q+(-1+\beta _{3})q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+\cdots$$
240.2.v.c $4$ $1.916$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$-4$$ $$4$$ $$q+(\zeta_{8}-\zeta_{8}^{3})q^{3}+(-1-2\zeta_{8})q^{5}+(1+\cdots)q^{7}+\cdots$$
240.2.v.d $4$ $1.916$ $$\Q(\zeta_{8})$$ None $$0$$ $$4$$ $$0$$ $$-12$$ $$q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$$
240.2.v.e $4$ $1.916$ $$\Q(\zeta_{8})$$ None $$0$$ $$4$$ $$0$$ $$4$$ $$q+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(240, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(240, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 2}$$