# Properties

 Label 966.2.i Level $966$ Weight $2$ Character orbit 966.i Rep. character $\chi_{966}(277,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $56$ Newform subspaces $14$ Sturm bound $384$ Trace bound $5$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$966 = 2 \cdot 3 \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 966.i (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$14$$ Sturm bound: $$384$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$, $$11$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(966, [\chi])$$.

Total New Old
Modular forms 400 56 344
Cusp forms 368 56 312
Eisenstein series 32 0 32

## Trace form

 $$56 q - 28 q^{4} + 8 q^{6} - 4 q^{7} - 28 q^{9} + O(q^{10})$$ $$56 q - 28 q^{4} + 8 q^{6} - 4 q^{7} - 28 q^{9} + 4 q^{10} + 16 q^{13} - 8 q^{14} - 8 q^{15} - 28 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 24 q^{22} - 4 q^{24} - 16 q^{25} - 4 q^{28} - 32 q^{29} - 4 q^{31} + 4 q^{33} + 40 q^{35} + 56 q^{36} + 8 q^{37} + 8 q^{38} - 8 q^{39} + 4 q^{40} - 16 q^{41} - 4 q^{42} + 32 q^{43} - 32 q^{47} - 44 q^{49} + 64 q^{50} - 8 q^{52} - 8 q^{53} - 4 q^{54} - 40 q^{55} - 8 q^{56} + 32 q^{57} - 28 q^{58} - 24 q^{59} + 4 q^{60} + 16 q^{61} + 32 q^{62} + 8 q^{63} + 56 q^{64} - 40 q^{65} - 32 q^{67} + 8 q^{68} + 16 q^{69} - 4 q^{70} + 80 q^{71} - 16 q^{73} - 32 q^{74} - 16 q^{76} + 48 q^{77} - 16 q^{78} + 4 q^{79} - 28 q^{81} - 80 q^{83} + 16 q^{84} + 96 q^{85} + 4 q^{87} + 12 q^{88} - 16 q^{89} - 8 q^{90} + 120 q^{91} - 16 q^{94} - 16 q^{95} - 4 q^{96} - 88 q^{97} - 16 q^{98} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(966, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
966.2.i.a $$2$$ $$7.714$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$-4$$ $$-5$$ $$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
966.2.i.b $$2$$ $$7.714$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$-1$$ $$0$$ $$1$$ $$q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
966.2.i.c $$2$$ $$7.714$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$-1$$ $$-1$$ $$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
966.2.i.d $$2$$ $$7.714$$ $$\Q(\sqrt{-3})$$ None $$-1$$ $$1$$ $$3$$ $$-5$$ $$q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
966.2.i.e $$2$$ $$7.714$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$-3$$ $$1$$ $$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
966.2.i.f $$2$$ $$7.714$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$-1$$ $$0$$ $$-1$$ $$q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
966.2.i.g $$2$$ $$7.714$$ $$\Q(\sqrt{-3})$$ None $$1$$ $$1$$ $$3$$ $$5$$ $$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots$$
966.2.i.h $$4$$ $$7.714$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$-2$$ $$-2$$ $$2$$ $$-2$$ $$q+\beta _{2}q^{2}+(-1-\beta _{2})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$$
966.2.i.i $$4$$ $$7.714$$ $$\Q(\sqrt{-3}, \sqrt{17})$$ None $$2$$ $$-2$$ $$1$$ $$2$$ $$q+\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots$$
966.2.i.j $$4$$ $$7.714$$ $$\Q(\sqrt{2}, \sqrt{-3})$$ None $$2$$ $$-2$$ $$2$$ $$-2$$ $$q+(1+\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots$$
966.2.i.k $$6$$ $$7.714$$ 6.0.29428272.1 None $$3$$ $$3$$ $$-3$$ $$-3$$ $$q+(1+\beta _{3})q^{2}-\beta _{3}q^{3}+\beta _{3}q^{4}+(-1+\cdots)q^{5}+\cdots$$
966.2.i.l $$8$$ $$7.714$$ 8.0.1768034304.4 None $$-4$$ $$-4$$ $$4$$ $$0$$ $$q+(-1-\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots$$
966.2.i.m $$8$$ $$7.714$$ $$\mathbb{Q}[x]/(x^{8} - \cdots)$$ None $$-4$$ $$4$$ $$-2$$ $$6$$ $$q+(-1-\beta _{1})q^{2}-\beta _{1}q^{3}+\beta _{1}q^{4}+(-1+\cdots)q^{5}+\cdots$$
966.2.i.n $$8$$ $$7.714$$ 8.0.$$\cdots$$.2 None $$4$$ $$4$$ $$-2$$ $$0$$ $$q+(1+\beta _{5})q^{2}-\beta _{5}q^{3}+\beta _{5}q^{4}-\beta _{1}q^{5}+\cdots$$

## Decomposition of $$S_{2}^{\mathrm{old}}(966, [\chi])$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(966, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(161, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(322, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(483, [\chi])$$$$^{\oplus 2}$$