# Properties

 Label 1575.2.bc Level $1575$ Weight $2$ Character orbit 1575.bc Rep. character $\chi_{1575}(899,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $96$ Newform subspaces $5$ Sturm bound $480$ Trace bound $11$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$1575 = 3^{2} \cdot 5^{2} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1575.bc (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$105$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$5$$ Sturm bound: $$480$$ Trace bound: $$11$$ Distinguishing $$T_p$$: $$2$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(1575, [\chi])$$.

Total New Old
Modular forms 528 96 432
Cusp forms 432 96 336
Eisenstein series 96 0 96

## Trace form

 $$96 q - 48 q^{4} + O(q^{10})$$ $$96 q - 48 q^{4} - 48 q^{16} - 12 q^{19} + 24 q^{31} + 24 q^{46} - 12 q^{49} - 12 q^{61} + 96 q^{64} - 24 q^{79} + 12 q^{91} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(1575, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1575.2.bc.a $8$ $12.576$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+(-\zeta_{24}^{4}+\zeta_{24}^{7})q^{2}+(3\zeta_{24}-2\zeta_{24}^{3}+\cdots)q^{7}+\cdots$$
1575.2.bc.b $8$ $12.576$ $$\Q(\zeta_{24})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+2\zeta_{24}^{2}q^{4}+(2\zeta_{24}+\zeta_{24}^{3})q^{7}-\zeta_{24}^{5}q^{11}+\cdots$$
1575.2.bc.c $24$ $12.576$ None $$0$$ $$0$$ $$0$$ $$0$$
1575.2.bc.d $24$ $12.576$ None $$0$$ $$0$$ $$0$$ $$0$$
1575.2.bc.e $32$ $12.576$ None $$0$$ $$0$$ $$0$$ $$0$$

## Decomposition of $$S_{2}^{\mathrm{old}}(1575, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(1575, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(105, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(315, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(525, [\chi])$$$$^{\oplus 2}$$