# Properties

 Label 960.3.l Level $960$ Weight $3$ Character orbit 960.l Rep. character $\chi_{960}(641,\cdot)$ Character field $\Q$ Dimension $64$ Newform subspaces $10$ Sturm bound $576$ Trace bound $9$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$960 = 2^{6} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 960.l (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$10$$ Sturm bound: $$576$$ Trace bound: $$9$$ Distinguishing $$T_p$$: $$7$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(960, [\chi])$$.

Total New Old
Modular forms 408 64 344
Cusp forms 360 64 296
Eisenstein series 48 0 48

## Trace form

 $$64 q + O(q^{10})$$ $$64 q + 32 q^{13} - 320 q^{25} + 32 q^{33} - 160 q^{37} + 448 q^{49} - 160 q^{57} + 192 q^{61} + 256 q^{81} + 160 q^{85} + 96 q^{93} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(960, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
960.3.l.a $2$ $26.158$ $$\Q(\sqrt{-5})$$ None $$0$$ $$-4$$ $$0$$ $$4$$ $$q+(-2-\beta )q^{3}-\beta q^{5}+2q^{7}+(-1+\cdots)q^{9}+\cdots$$
960.3.l.b $2$ $26.158$ $$\Q(\sqrt{-5})$$ None $$0$$ $$-4$$ $$0$$ $$12$$ $$q+(-2+\beta )q^{3}-\beta q^{5}+6q^{7}+(-1+\cdots)q^{9}+\cdots$$
960.3.l.c $2$ $26.158$ $$\Q(\sqrt{-5})$$ None $$0$$ $$4$$ $$0$$ $$-12$$ $$q+(2+\beta )q^{3}+\beta q^{5}-6q^{7}+(-1+4\beta )q^{9}+\cdots$$
960.3.l.d $2$ $26.158$ $$\Q(\sqrt{-5})$$ None $$0$$ $$4$$ $$0$$ $$-4$$ $$q+(2+\beta )q^{3}-\beta q^{5}-2q^{7}+(-1+4\beta )q^{9}+\cdots$$
960.3.l.e $4$ $26.158$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None $$0$$ $$-4$$ $$0$$ $$8$$ $$q+(-1-\beta _{1}+\beta _{2})q^{3}-\beta _{2}q^{5}+(2-5\beta _{1}+\cdots)q^{7}+\cdots$$
960.3.l.f $4$ $26.158$ $$\Q(\sqrt{-2}, \sqrt{-5})$$ None $$0$$ $$4$$ $$0$$ $$-8$$ $$q+(1-\beta _{1}-\beta _{2})q^{3}-\beta _{2}q^{5}+(-2-5\beta _{1}+\cdots)q^{7}+\cdots$$
960.3.l.g $8$ $26.158$ 8.0.$$\cdots$$.5 None $$0$$ $$-4$$ $$0$$ $$-16$$ $$q+\beta _{2}q^{3}-\beta _{6}q^{5}+(-1-\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots$$
960.3.l.h $8$ $26.158$ 8.0.$$\cdots$$.5 None $$0$$ $$4$$ $$0$$ $$16$$ $$q+\beta _{3}q^{3}+\beta _{4}q^{5}+(3-\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{7}+\cdots$$
960.3.l.i $16$ $26.158$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{8}q^{3}+\beta _{5}q^{5}+(-\beta _{8}-\beta _{9})q^{7}+\cdots$$
960.3.l.j $16$ $26.158$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{3}+\beta _{4}q^{5}+(\beta _{1}+\beta _{5})q^{7}+(1+\cdots)q^{9}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(960, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(960, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(15, [\chi])$$$$^{\oplus 7}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(24, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(30, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(48, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(96, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(120, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(192, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(240, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(480, [\chi])$$$$^{\oplus 2}$$