# Properties

 Label 966.2.l Level $966$ Weight $2$ Character orbit 966.l Rep. character $\chi_{966}(47,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $120$ Newform subspaces $4$ Sturm bound $384$ Trace bound $3$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$966 = 2 \cdot 3 \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 966.l (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$21$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$4$$ Sturm bound: $$384$$ Trace bound: $$3$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

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

Total New Old
Modular forms 400 120 280
Cusp forms 368 120 248
Eisenstein series 32 0 32

## Trace form

 $$120 q + 60 q^{4} + 20 q^{7} + 8 q^{9} + O(q^{10})$$ $$120 q + 60 q^{4} + 20 q^{7} + 8 q^{9} + 12 q^{10} - 40 q^{15} - 60 q^{16} - 24 q^{19} + 12 q^{21} - 8 q^{22} - 64 q^{25} + 4 q^{28} + 12 q^{30} + 12 q^{31} + 60 q^{33} + 16 q^{36} - 8 q^{37} + 20 q^{39} + 12 q^{40} + 8 q^{42} + 16 q^{43} - 12 q^{45} - 4 q^{49} - 28 q^{51} - 24 q^{52} + 56 q^{57} - 28 q^{58} - 20 q^{60} - 72 q^{61} - 24 q^{63} - 120 q^{64} - 16 q^{67} - 52 q^{70} + 24 q^{73} - 48 q^{75} + 64 q^{78} - 20 q^{79} + 40 q^{81} - 12 q^{84} + 80 q^{85} + 12 q^{87} - 4 q^{88} + 32 q^{91} + 16 q^{93} - 24 q^{94} - 64 q^{99} + O(q^{100})$$

## 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.l.a $4$ $7.714$ $$\Q(\zeta_{12})$$ None $$0$$ $$0$$ $$0$$ $$2$$ $$q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-2\zeta_{12}^{3})q^{3}+\cdots$$
966.2.l.b $4$ $7.714$ $$\Q(\zeta_{12})$$ None $$0$$ $$6$$ $$0$$ $$-10$$ $$q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(1+\zeta_{12}^{2})q^{3}+\cdots$$
966.2.l.c $56$ $7.714$ None $$0$$ $$-6$$ $$0$$ $$20$$
966.2.l.d $56$ $7.714$ None $$0$$ $$0$$ $$0$$ $$8$$

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

$$S_{2}^{\mathrm{old}}(966, [\chi]) \simeq$$ $$S_{2}^{\mathrm{new}}(21, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(42, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(483, [\chi])$$$$^{\oplus 2}$$