# Properties

 Label 966.2.bf Level $966$ Weight $2$ Character orbit 966.bf Rep. character $\chi_{966}(11,\cdot)$ Character field $\Q(\zeta_{66})$ Dimension $1280$ Newform subspaces $1$ Sturm bound $384$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$966 = 2 \cdot 3 \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 966.bf (of order $$66$$ and degree $$20$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$483$$ Character field: $$\Q(\zeta_{66})$$ Newform subspaces: $$1$$ Sturm bound: $$384$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 4000 1280 2720
Cusp forms 3680 1280 2400
Eisenstein series 320 0 320

## Trace form

 $$1280q - 64q^{4} - 8q^{6} + 4q^{9} + O(q^{10})$$ $$1280q - 64q^{4} - 8q^{6} + 4q^{9} + 64q^{16} + 44q^{18} - 132q^{21} - 4q^{24} + 72q^{25} + 108q^{27} + 44q^{30} + 8q^{36} + 44q^{37} - 4q^{39} - 88q^{43} - 12q^{46} + 60q^{49} - 48q^{54} + 96q^{55} + 44q^{58} - 176q^{61} - 110q^{63} + 128q^{64} + 56q^{69} - 120q^{70} + 44q^{72} + 40q^{73} - 268q^{75} + 16q^{78} + 88q^{79} + 8q^{81} - 56q^{82} - 22q^{84} + 64q^{85} - 42q^{87} - 32q^{93} + 8q^{94} + 4q^{96} + 132q^{99} + O(q^{100})$$

## 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.bf.a $$1280$$ $$7.714$$ None $$0$$ $$0$$ $$0$$ $$0$$

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

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