# Properties

 Label 240.2.f Level $240$ Weight $2$ Character orbit 240.f Rep. character $\chi_{240}(49,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $3$ Sturm bound $96$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$240 = 2^{4} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 240.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$96$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$7$$, $$13$$

## Dimensions

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

Total New Old
Modular forms 60 6 54
Cusp forms 36 6 30
Eisenstein series 24 0 24

## Trace form

 $$6 q + 2 q^{5} - 6 q^{9} + O(q^{10})$$ $$6 q + 2 q^{5} - 6 q^{9} + 16 q^{19} + 6 q^{25} - 4 q^{29} + 8 q^{31} - 24 q^{35} - 8 q^{39} - 12 q^{41} - 2 q^{45} - 6 q^{49} - 16 q^{51} + 8 q^{55} + 16 q^{59} + 12 q^{61} - 8 q^{65} - 8 q^{69} - 16 q^{71} + 8 q^{75} - 40 q^{79} + 6 q^{81} + 8 q^{85} + 28 q^{89} - 16 q^{91} + 32 q^{95} + O(q^{100})$$

## 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.f.a $2$ $1.916$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+iq^{3}+(-2+i)q^{5}+2iq^{7}-q^{9}+\cdots$$
240.2.f.b $2$ $1.916$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{3}+(1-2i)q^{5}-4iq^{7}-q^{9}+\cdots$$
240.2.f.c $2$ $1.916$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+iq^{3}+(2+i)q^{5}+2iq^{7}-q^{9}-2q^{11}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(240, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 2}$$