# Properties

 Label 240.2.h Level $240$ Weight $2$ Character orbit 240.h Rep. character $\chi_{240}(191,\cdot)$ Character field $\Q$ Dimension $8$ Newform subspaces $2$ Sturm bound $96$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$240 = 2^{4} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 240.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$12$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$96$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

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

Total New Old
Modular forms 60 8 52
Cusp forms 36 8 28
Eisenstein series 24 0 24

## Trace form

 $$8 q + 12 q^{9} + O(q^{10})$$ $$8 q + 12 q^{9} + 8 q^{13} - 12 q^{21} - 8 q^{25} - 8 q^{37} + 12 q^{45} - 16 q^{49} - 24 q^{57} - 8 q^{61} - 36 q^{69} - 64 q^{73} + 48 q^{93} + 80 q^{97} + O(q^{100})$$

## 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.h.a $4$ $1.916$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{2}q^{5}+(\beta _{1}+\beta _{3})q^{7}+3\beta _{2}q^{9}+\cdots$$
240.2.h.b $4$ $1.916$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{3}q^{3}-\zeta_{12}q^{5}+2\zeta_{12}^{2}q^{7}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(240, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 3}$$