# Properties

 Label 966.2.k Level $966$ Weight $2$ Character orbit 966.k Rep. character $\chi_{966}(229,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $64$ Newform subspaces $2$ Sturm bound $384$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$966 = 2 \cdot 3 \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 966.k (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$161$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$2$$ Sturm bound: $$384$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 400 64 336
Cusp forms 368 64 304
Eisenstein series 32 0 32

## Trace form

 $$64q - 32q^{4} + 32q^{9} + O(q^{10})$$ $$64q - 32q^{4} + 32q^{9} - 32q^{16} + 12q^{23} - 64q^{25} - 24q^{26} + 16q^{29} + 24q^{31} - 8q^{35} - 64q^{36} + 4q^{46} + 24q^{47} + 48q^{49} - 32q^{50} + 16q^{58} - 24q^{59} + 64q^{64} + 88q^{70} + 64q^{71} - 72q^{73} + 48q^{75} + 24q^{77} + 32q^{78} - 32q^{81} - 48q^{82} - 80q^{85} - 72q^{87} - 24q^{92} - 8q^{93} + 40q^{95} + O(q^{100})$$

## 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.k.a $$32$$ $$7.714$$ None $$-16$$ $$0$$ $$0$$ $$0$$
966.2.k.b $$32$$ $$7.714$$ None $$16$$ $$0$$ $$0$$ $$0$$

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

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