# Properties

 Label 966.2.be Level $966$ Weight $2$ Character orbit 966.be Rep. character $\chi_{966}(19,\cdot)$ Character field $\Q(\zeta_{66})$ Dimension $640$ 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.be (of order $$66$$ and degree $$20$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$161$$ Character field: $$\Q(\zeta_{66})$$ 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 4000 640 3360
Cusp forms 3680 640 3040
Eisenstein series 320 0 320

## Trace form

 $$640 q + 32 q^{4} - 32 q^{9} + O(q^{10})$$ $$640 q + 32 q^{4} - 32 q^{9} + 32 q^{16} + 76 q^{23} - 24 q^{25} + 24 q^{26} + 88 q^{28} - 16 q^{29} - 24 q^{31} + 52 q^{35} + 64 q^{36} - 44 q^{37} + 88 q^{43} - 4 q^{46} - 24 q^{47} - 48 q^{49} + 32 q^{50} - 44 q^{51} + 88 q^{57} + 28 q^{58} + 24 q^{59} - 64 q^{64} - 64 q^{71} + 72 q^{73} - 48 q^{75} - 24 q^{77} - 32 q^{78} + 88 q^{79} + 32 q^{81} + 48 q^{82} - 8 q^{85} + 72 q^{87} + 24 q^{92} + 8 q^{93} + 92 q^{95} - 88 q^{98} + 88 q^{99} + O(q^{100})$$

## 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.be.a $320$ $7.714$ None $$-16$$ $$0$$ $$0$$ $$0$$
966.2.be.b $320$ $7.714$ None $$16$$ $$0$$ $$0$$ $$0$$

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

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