# Properties

 Label 966.2.g Level $966$ Weight $2$ Character orbit 966.g Rep. character $\chi_{966}(643,\cdot)$ Character field $\Q$ Dimension $32$ Newform subspaces $5$ Sturm bound $384$ Trace bound $25$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$966 = 2 \cdot 3 \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 966.g (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$161$$ Character field: $$\Q$$ Newform subspaces: $$5$$ Sturm bound: $$384$$ Trace bound: $$25$$ Distinguishing $$T_p$$: $$5$$, $$11$$

## Dimensions

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

Total New Old
Modular forms 200 32 168
Cusp forms 184 32 152
Eisenstein series 16 0 16

## Trace form

 $$32 q + 32 q^{4} - 32 q^{9} + O(q^{10})$$ $$32 q + 32 q^{4} - 32 q^{9} + 32 q^{16} + 40 q^{25} + 32 q^{29} - 16 q^{35} - 32 q^{36} - 16 q^{46} + 32 q^{50} + 8 q^{58} + 32 q^{64} - 16 q^{70} - 64 q^{71} + 48 q^{77} - 8 q^{78} + 32 q^{81} + 80 q^{85} + 8 q^{93} + 80 q^{95} + O(q^{100})$$

## 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.g.a $4$ $7.714$ $$\Q(i, \sqrt{14})$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}+\beta _{1}q^{7}+\cdots$$
966.2.g.b $4$ $7.714$ $$\Q(i, \sqrt{14})$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+\beta _{2}q^{3}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$$
966.2.g.c $4$ $7.714$ $$\Q(i, \sqrt{7})$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+\beta _{3}q^{7}+\cdots$$
966.2.g.d $4$ $7.714$ $$\Q(i, \sqrt{7})$$ None $$-4$$ $$0$$ $$0$$ $$0$$ $$q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots$$
966.2.g.e $16$ $7.714$ $$\mathbb{Q}[x]/(x^{16} + \cdots)$$ None $$16$$ $$0$$ $$0$$ $$0$$ $$q+q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{8}q^{5}+\beta _{2}q^{6}+\cdots$$

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

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