# Properties

 Label 480.2.f Level $480$ Weight $2$ Character orbit 480.f Rep. character $\chi_{480}(289,\cdot)$ Character field $\Q$ Dimension $12$ Newform subspaces $5$ Sturm bound $192$ Trace bound $15$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$480 = 2^{5} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 480.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$192$$ Trace bound: $$15$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$19$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(480, [\chi])$$.

Total New Old
Modular forms 112 12 100
Cusp forms 80 12 68
Eisenstein series 32 0 32

## Trace form

 $$12 q - 4 q^{5} - 12 q^{9} + O(q^{10})$$ $$12 q - 4 q^{5} - 12 q^{9} - 20 q^{25} + 8 q^{29} + 40 q^{41} + 4 q^{45} - 12 q^{49} - 8 q^{61} + 12 q^{81} - 64 q^{85} - 40 q^{89} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(480, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
480.2.f.a $2$ $3.833$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+iq^{3}+(-2+i)q^{5}-2iq^{7}-q^{9}+\cdots$$
480.2.f.b $2$ $3.833$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+iq^{3}+(-2-i)q^{5}-2iq^{7}-q^{9}+\cdots$$
480.2.f.c $2$ $3.833$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{3}+(1+2i)q^{5}+4iq^{7}-q^{9}+\cdots$$
480.2.f.d $2$ $3.833$ $$\Q(\sqrt{-1})$$ None $$0$$ $$0$$ $$2$$ $$0$$ $$q+iq^{3}+(1-2i)q^{5}+4iq^{7}-q^{9}+\cdots$$
480.2.f.e $4$ $3.833$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{2}q^{5}-2\beta _{1}q^{7}-q^{9}-2\beta _{3}q^{11}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(480, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(480, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(240, [\chi])$$$$^{\oplus 2}$$