# Properties

 Label 960.3.j Level $960$ Weight $3$ Character orbit 960.j Rep. character $\chi_{960}(319,\cdot)$ Character field $\Q$ Dimension $48$ Newform subspaces $7$ 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.j (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$20$$ Character field: $$\Q$$ Newform subspaces: $$7$$ Sturm bound: $$576$$ Trace bound: $$15$$ Distinguishing $$T_p$$: $$7$$, $$11$$

## Dimensions

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

Total New Old
Modular forms 408 48 360
Cusp forms 360 48 312
Eisenstein series 48 0 48

## Trace form

 $$48q + 144q^{9} + O(q^{10})$$ $$48q + 144q^{9} + 48q^{25} + 160q^{41} + 336q^{49} + 32q^{61} + 96q^{65} + 96q^{69} + 432q^{81} + 288q^{85} + 160q^{89} + O(q^{100})$$

## 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.j.a $$4$$ $$26.158$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$-16$$ $$0$$ $$q+\zeta_{12}^{2}q^{3}+(-4-\zeta_{12}^{3})q^{5}-2\zeta_{12}^{2}q^{7}+\cdots$$
960.3.j.b $$4$$ $$26.158$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$0$$ $$q-\zeta_{12}^{3}q^{3}-5\zeta_{12}q^{5}-6\zeta_{12}^{3}q^{7}+\cdots$$
960.3.j.c $$4$$ $$26.158$$ $$\Q(\sqrt{3}, \sqrt{-7})$$ None $$0$$ $$0$$ $$8$$ $$0$$ $$q+\beta _{1}q^{3}+(2-\beta _{2})q^{5}-2\beta _{1}q^{7}+3q^{9}+\cdots$$
960.3.j.d $$4$$ $$26.158$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$20$$ $$0$$ $$q-\zeta_{12}q^{3}+5q^{5}-4\zeta_{12}q^{7}+3q^{9}+\cdots$$
960.3.j.e $$8$$ $$26.158$$ 8.0.$$\cdots$$.4 None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{1}q^{3}+(-1+\beta _{3})q^{5}+(-3\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots$$
960.3.j.f $$12$$ $$26.158$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q-\beta _{1}q^{3}+(\beta _{1}-\beta _{6})q^{5}+(\beta _{5}-\beta _{8})q^{7}+\cdots$$
960.3.j.g $$12$$ $$26.158$$ $$\mathbb{Q}[x]/(x^{12} - \cdots)$$ None $$0$$ $$0$$ $$-4$$ $$0$$ $$q+\beta _{1}q^{3}+(\beta _{1}-\beta _{8})q^{5}+(-\beta _{5}+\beta _{8}+\cdots)q^{7}+\cdots$$

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

$$S_{3}^{\mathrm{old}}(960, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(20, [\chi])$$$$^{\oplus 10}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(60, [\chi])$$$$^{\oplus 5}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(80, [\chi])$$$$^{\oplus 6}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(160, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(240, [\chi])$$$$^{\oplus 3}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(320, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{3}^{\mathrm{new}}(480, [\chi])$$$$^{\oplus 2}$$