# Properties

 Label 1440.2.h Level $1440$ Weight $2$ Character orbit 1440.h Rep. character $\chi_{1440}(1151,\cdot)$ Character field $\Q$ Dimension $16$ Newform subspaces $4$ Sturm bound $576$ Trace bound $23$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1440 = 2^{5} \cdot 3^{2} \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1440.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$12$$ Character field: $$\Q$$ Newform subspaces: $$4$$ Sturm bound: $$576$$ Trace bound: $$23$$ Distinguishing $$T_p$$: $$11$$, $$23$$

## Dimensions

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

Total New Old
Modular forms 320 16 304
Cusp forms 256 16 240
Eisenstein series 64 0 64

## Trace form

 $$16 q + O(q^{10})$$ $$16 q - 32 q^{13} - 16 q^{25} + 32 q^{37} + 16 q^{49} + 32 q^{61} - 32 q^{73} - 32 q^{97} + O(q^{100})$$

## 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.h.a $4$ $11.498$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2})q^{7}+(-4-\zeta_{8}^{3})q^{11}+\cdots$$
1440.2.h.b $4$ $11.498$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2})q^{7}-\zeta_{8}^{3}q^{11}+\cdots$$
1440.2.h.c $4$ $11.498$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2})q^{7}+\zeta_{8}^{3}q^{11}+\cdots$$
1440.2.h.d $4$ $11.498$ $$\Q(\zeta_{8})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2})q^{7}+(4+\zeta_{8}^{3})q^{11}+\cdots$$

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

$$S_{2}^{\mathrm{old}}(1440, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(36, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(144, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(180, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(240, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(288, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(480, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(720, [\chi])$$$$^{\oplus 2}$$