# Properties

 Label 1440.2.bi Level $1440$ Weight $2$ Character orbit 1440.bi Rep. character $\chi_{1440}(847,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $56$ Newform subspaces $5$ Sturm bound $576$ Trace bound $7$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1440 = 2^{5} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1440.bi (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$40$$ Character field: $$\Q(i)$$ Newform subspaces: $$5$$ Sturm bound: $$576$$ Trace bound: $$7$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1440, [\chi])$$.

Total New Old
Modular forms 640 64 576
Cusp forms 512 56 456
Eisenstein series 128 8 120

## Trace form

 $$56 q + O(q^{10})$$ $$56 q - 8 q^{11} - 28 q^{35} + 8 q^{41} + 36 q^{43} + 8 q^{65} + 28 q^{67} + 16 q^{73} + 36 q^{83} + 40 q^{91} - 16 q^{97} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1440, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1440.2.bi.a $4$ $11.498$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$-4$$ $$q+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(-1+\zeta_{8}^{2})q^{7}+\cdots$$
1440.2.bi.b $4$ $11.498$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$4$$ $$q+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+(1-\zeta_{8}^{2})q^{7}+\cdots$$
1440.2.bi.c $8$ $11.498$ $$\Q(\zeta_{20})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{20}^{4}-\zeta_{20}^{5}-\zeta_{20}^{6}+\zeta_{20}^{7})q^{5}+\cdots$$
1440.2.bi.d $16$ $11.498$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{9}q^{5}-\beta _{10}q^{7}-\beta _{15}q^{11}+\beta _{7}q^{13}+\cdots$$
1440.2.bi.e $24$ $11.498$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1440, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1440, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(40, [\chi])$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(360, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(480, [\chi])$$$$^{\oplus 2}$$