# Properties

 Label 966.2.f Level $966$ Weight $2$ Character orbit 966.f Rep. character $\chi_{966}(461,\cdot)$ Character field $\Q$ Dimension $56$ Newform subspaces $3$ Sturm bound $384$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$966 = 2 \cdot 3 \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 966.f (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$384$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 200 56 144
Cusp forms 184 56 128
Eisenstein series 16 0 16

## Trace form

 $$56q - 56q^{4} + 8q^{7} - 8q^{9} + O(q^{10})$$ $$56q - 56q^{4} + 8q^{7} - 8q^{9} + 16q^{15} + 56q^{16} - 12q^{21} + 8q^{22} + 48q^{25} - 8q^{28} + 24q^{30} + 8q^{36} + 40q^{37} + 40q^{39} + 28q^{42} + 40q^{43} - 24q^{49} - 8q^{51} - 56q^{57} - 56q^{58} - 16q^{60} + 24q^{63} - 56q^{64} - 88q^{67} - 32q^{70} - 16q^{78} + 48q^{79} + 8q^{81} + 12q^{84} + 64q^{85} - 8q^{88} - 8q^{91} - 16q^{93} + 64q^{99} + O(q^{100})$$

## 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.f.a $$4$$ $$7.714$$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$8$$ $$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}-q^{4}-\zeta_{12}^{3}q^{5}+\cdots$$
966.2.f.b $$24$$ $$7.714$$ None $$0$$ $$0$$ $$0$$ $$-4$$
966.2.f.c $$28$$ $$7.714$$ None $$0$$ $$0$$ $$0$$ $$4$$

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

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