# Properties

 Label 966.2.q Level $966$ Weight $2$ Character orbit 966.q Rep. character $\chi_{966}(85,\cdot)$ Character field $\Q(\zeta_{11})$ Dimension $240$ Newform subspaces $10$ 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.q (of order $$11$$ and degree $$10$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$23$$ Character field: $$\Q(\zeta_{11})$$ Newform subspaces: $$10$$ Sturm bound: $$384$$ Trace bound: $$5$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 2000 240 1760
Cusp forms 1840 240 1600
Eisenstein series 160 0 160

## Trace form

 $$240q - 24q^{4} - 24q^{9} + O(q^{10})$$ $$240q - 24q^{4} - 24q^{9} - 16q^{11} - 32q^{13} - 16q^{15} - 24q^{16} + 56q^{17} + 56q^{19} - 4q^{21} + 72q^{22} + 56q^{23} + 24q^{25} + 72q^{26} + 56q^{29} - 16q^{30} + 40q^{31} - 16q^{33} - 16q^{34} - 16q^{35} - 24q^{36} + 12q^{37} - 32q^{38} + 72q^{39} + 56q^{41} - 4q^{42} - 4q^{43} - 16q^{44} - 24q^{46} + 112q^{47} - 24q^{49} - 16q^{50} + 28q^{51} - 32q^{52} + 40q^{53} + 112q^{55} + 28q^{57} - 40q^{58} - 64q^{59} - 16q^{60} - 48q^{61} - 32q^{62} - 24q^{64} - 48q^{65} - 32q^{66} + 24q^{67} - 32q^{68} - 16q^{69} - 8q^{70} - 80q^{71} - 8q^{73} - 32q^{75} - 32q^{76} - 8q^{78} - 40q^{79} - 24q^{81} - 32q^{82} + 56q^{83} - 4q^{84} + 24q^{85} - 32q^{86} - 32q^{87} - 16q^{88} + 24q^{89} + 72q^{91} - 32q^{92} - 56q^{93} - 16q^{94} - 8q^{95} - 8q^{97} - 16q^{99} + O(q^{100})$$

## 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.q.a $$10$$ $$7.714$$ $$\Q(\zeta_{22})$$ None $$-1$$ $$-1$$ $$-14$$ $$1$$ $$q+\zeta_{22}^{4}q^{2}+(-1+\zeta_{22}-\zeta_{22}^{2}+\zeta_{22}^{3}+\cdots)q^{3}+\cdots$$
966.2.q.b $$10$$ $$7.714$$ $$\Q(\zeta_{22})$$ None $$-1$$ $$-1$$ $$2$$ $$1$$ $$q+\zeta_{22}^{4}q^{2}+(-1+\zeta_{22}-\zeta_{22}^{2}+\zeta_{22}^{3}+\cdots)q^{3}+\cdots$$
966.2.q.c $$10$$ $$7.714$$ $$\Q(\zeta_{22})$$ None $$1$$ $$-1$$ $$0$$ $$-1$$ $$q-\zeta_{22}^{4}q^{2}+(-1+\zeta_{22}-\zeta_{22}^{2}+\zeta_{22}^{3}+\cdots)q^{3}+\cdots$$
966.2.q.d $$20$$ $$7.714$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$-2$$ $$2$$ $$12$$ $$-2$$ $$q-\beta _{7}q^{2}-\beta _{19}q^{3}-\beta _{15}q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$$
966.2.q.e $$20$$ $$7.714$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$2$$ $$-2$$ $$10$$ $$-2$$ $$q+\beta _{17}q^{2}+(-1-\beta _{4}-\beta _{5}+\beta _{6}+\beta _{7}+\cdots)q^{3}+\cdots$$
966.2.q.f $$30$$ $$7.714$$ None $$3$$ $$-3$$ $$-10$$ $$3$$
966.2.q.g $$30$$ $$7.714$$ None $$3$$ $$3$$ $$-10$$ $$3$$
966.2.q.h $$30$$ $$7.714$$ None $$3$$ $$3$$ $$10$$ $$-3$$
966.2.q.i $$40$$ $$7.714$$ None $$-4$$ $$-4$$ $$4$$ $$-4$$
966.2.q.j $$40$$ $$7.714$$ None $$-4$$ $$4$$ $$-4$$ $$4$$

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

$$S_{2}^{\mathrm{old}}(966, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(23, [\chi])$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(46, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(69, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(138, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(161, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(322, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(483, [\chi])$$$$^{\oplus 2}$$