# Properties

 Label 720.2.f Level $720$ Weight $2$ Character orbit 720.f Rep. character $\chi_{720}(289,\cdot)$ Character field $\Q$ Dimension $14$ Newform subspaces $7$ Sturm bound $288$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$720 = 2^{4} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 720.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$288$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$13$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(720, [\chi])$$.

Total New Old
Modular forms 168 16 152
Cusp forms 120 14 106
Eisenstein series 48 2 46

## Trace form

 $$14 q + O(q^{10})$$ $$14 q - 8 q^{11} + 2 q^{25} + 8 q^{29} - 8 q^{31} + 16 q^{35} + 8 q^{41} - 22 q^{49} + 32 q^{55} + 8 q^{59} + 4 q^{61} - 8 q^{65} + 32 q^{71} - 8 q^{79} + 12 q^{85} - 16 q^{89} + 32 q^{91} - 40 q^{95} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(720, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
720.2.f.a $2$ $5.749$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-2+i)q^{5}+4iq^{7}-4q^{11}-4iq^{13}+\cdots$$
720.2.f.b $2$ $5.749$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+(-2+i)q^{5}-2iq^{7}+2q^{11}+2iq^{13}+\cdots$$
720.2.f.c $2$ $5.749$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-2$$ $$0$$ $$q+(-1+i)q^{5}-2iq^{7}-4q^{11}-2iq^{17}+\cdots$$
720.2.f.d $2$ $5.749$ $$\Q(\sqrt{-5})$$ $$\Q(\sqrt{-15})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta q^{5}+2\beta q^{17}+4q^{19}+4\beta q^{23}+\cdots$$
720.2.f.e $2$ $5.749$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+(1+i)q^{5}+iq^{7}-4q^{11}+2iq^{13}+\cdots$$
720.2.f.f $2$ $5.749$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2+i)q^{5}-2iq^{7}+2q^{11}-6iq^{13}+\cdots$$
720.2.f.g $2$ $5.749$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$4$$ $$0$$ $$q+(2+i)q^{5}-4iq^{7}+4q^{11}+4iq^{13}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(720, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(720, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(45, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(90, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(180, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(240, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(360, [\chi])$$$$^{\oplus 2}$$