# Properties

 Label 240.2.w Level $240$ Weight $2$ Character orbit 240.w Rep. character $\chi_{240}(127,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $12$ Newform subspaces $2$ Sturm bound $96$ Trace bound $1$

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## Defining parameters

 Level: $$N$$ $$=$$ $$240 = 2^{4} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 240.w (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$20$$ Character field: $$\Q(i)$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

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

Total New Old
Modular forms 120 12 108
Cusp forms 72 12 60
Eisenstein series 48 0 48

## Trace form

 $$12 q + O(q^{10})$$ $$12 q + 12 q^{13} + 12 q^{17} + 12 q^{25} - 24 q^{33} - 12 q^{37} - 48 q^{41} - 12 q^{45} - 12 q^{53} - 12 q^{65} + 12 q^{73} - 48 q^{77} - 12 q^{81} - 36 q^{85} + 48 q^{93} + 12 q^{97} + O(q^{100})$$

## 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.w.a $4$ $1.916$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$-8$$ $$0$$ $$q+\zeta_{8}q^{3}+(-2+\zeta_{8}^{2})q^{5}+4\zeta_{8}^{3}q^{7}+\cdots$$
240.2.w.b $8$ $1.916$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$8$$ $$0$$ $$q+\zeta_{24}^{5}q^{3}+(1+\zeta_{24}^{2}-\zeta_{24}^{3})q^{5}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(240, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(20, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 2}$$