# Properties

 Label 960.2.h Level $960$ Weight $2$ Character orbit 960.h Rep. character $\chi_{960}(191,\cdot)$ Character field $\Q$ Dimension $32$ Newform subspaces $7$ Sturm bound $384$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$960 = 2^{6} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 960.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$12$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$384$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$7$$, $$11$$, $$23$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(960, [\chi])$$.

Total New Old
Modular forms 216 32 184
Cusp forms 168 32 136
Eisenstein series 48 0 48

## Trace form

 $$32 q + O(q^{10})$$ $$32 q - 16 q^{13} - 32 q^{25} + 16 q^{33} + 16 q^{37} - 32 q^{49} - 16 q^{57} + 32 q^{61} - 16 q^{85} - 48 q^{93} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(960, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
960.2.h.a $4$ $7.666$ $$\Q(\zeta_{8})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(-1+\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(2\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots$$
960.2.h.b $4$ $7.666$ $$\Q(\zeta_{8})$$ None $$0$$ $$-4$$ $$0$$ $$0$$ $$q+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{5}+\cdots$$
960.2.h.c $4$ $7.666$ $$\Q(i, \sqrt{6})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{3})q^{7}+3\beta _{2}q^{9}+\cdots$$
960.2.h.d $4$ $7.666$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\zeta_{12}^{3}q^{3}-\zeta_{12}q^{5}-2\zeta_{12}^{2}q^{7}+\cdots$$
960.2.h.e $4$ $7.666$ $$\Q(\zeta_{8})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(1+\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}+(2\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots$$
960.2.h.f $4$ $7.666$ $$\Q(\zeta_{8})$$ None $$0$$ $$4$$ $$0$$ $$0$$ $$q+(1+\zeta_{8}-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots$$
960.2.h.g $8$ $7.666$ 8.0.342102016.5 None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{3}-\beta _{1}q^{5}+(\beta _{3}+\beta _{4})q^{7}+\beta _{6}q^{9}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(960, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(960, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(240, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(480, [\chi])$$$$^{\oplus 2}$$