# Properties

 Label 960.3.c Level $960$ Weight $3$ Character orbit 960.c Rep. character $\chi_{960}(449,\cdot)$ Character field $\Q$ Dimension $92$ Newform subspaces $13$ Sturm bound $576$ Trace bound $15$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$960 = 2^{6} \cdot 3 \cdot 5$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 960.c (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$15$$ Character field: $$\Q$$ Newform subspaces: $$13$$ Sturm bound: $$576$$ Trace bound: $$15$$ Distinguishing $$T_p$$: $$7$$, $$17$$, $$19$$

## Dimensions

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

Total New Old
Modular forms 408 100 308
Cusp forms 360 92 268
Eisenstein series 48 8 40

## Trace form

 $$92 q - 4 q^{9} + O(q^{10})$$ $$92 q - 4 q^{9} - 32 q^{21} - 4 q^{25} - 96 q^{45} - 484 q^{49} + 40 q^{61} - 440 q^{69} - 36 q^{81} + 104 q^{85} + O(q^{100})$$

## 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.c.a $1$ $26.158$ $$\Q$$ $$\Q(\sqrt{-15})$$ $$0$$ $$-3$$ $$-5$$ $$0$$ $$q-3q^{3}-5q^{5}+9q^{9}+15q^{15}-14q^{17}+\cdots$$
960.3.c.b $1$ $26.158$ $$\Q$$ $$\Q(\sqrt{-15})$$ $$0$$ $$-3$$ $$5$$ $$0$$ $$q-3q^{3}+5q^{5}+9q^{9}-15q^{15}+14q^{17}+\cdots$$
960.3.c.c $1$ $26.158$ $$\Q$$ $$\Q(\sqrt{-15})$$ $$0$$ $$3$$ $$-5$$ $$0$$ $$q+3q^{3}-5q^{5}+9q^{9}-15q^{15}-14q^{17}+\cdots$$
960.3.c.d $1$ $26.158$ $$\Q$$ $$\Q(\sqrt{-15})$$ $$0$$ $$3$$ $$5$$ $$0$$ $$q+3q^{3}+5q^{5}+9q^{9}+15q^{15}+14q^{17}+\cdots$$
960.3.c.e $4$ $26.158$ $$\Q(\sqrt{2}, \sqrt{-17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+(-2\beta _{2}-\beta _{3})q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots$$
960.3.c.f $4$ $26.158$ $$\Q(\sqrt{2}, \sqrt{-17})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\beta _{1}q^{3}+(2\beta _{2}-\beta _{3})q^{5}+(-2\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$$
960.3.c.g $4$ $26.158$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+(\beta _{1}-\beta _{3})q^{5}+(-2\beta _{2}+2\beta _{3})q^{7}+\cdots$$
960.3.c.h $4$ $26.158$ $$\Q(i, \sqrt{5})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{2}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-2\beta _{2}+2\beta _{3})q^{7}+\cdots$$
960.3.c.i $8$ $26.158$ 8.0.40960000.1 $$\Q(\sqrt{-5})$$ $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{5}q^{3}+5\beta _{1}q^{5}+(2\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{7}+\cdots$$
960.3.c.j $12$ $26.158$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}+\beta _{8}q^{5}+\beta _{9}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots$$
960.3.c.k $12$ $26.158$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{1}q^{3}-\beta _{7}q^{5}-\beta _{9}q^{7}+(1-\beta _{4}+\cdots)q^{9}+\cdots$$
960.3.c.l $16$ $26.158$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q+\beta _{3}q^{3}+(\beta _{7}+\beta _{10})q^{5}+(\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots$$
960.3.c.m $24$ $26.158$ None $$0$$ $$0$$ $$0$$ $$0$$

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

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