# Properties

 Label 966.2.h Level $966$ Weight $2$ Character orbit 966.h Rep. character $\chi_{966}(827,\cdot)$ Character field $\Q$ Dimension $48$ Newform subspaces $2$ Sturm bound $384$ Trace bound $5$

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## Defining parameters

 Level: $$N$$ $$=$$ $$966 = 2 \cdot 3 \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 966.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$69$$ Character field: $$\Q$$ Newform subspaces: $$2$$ Sturm bound: $$384$$ Trace bound: $$5$$

## Dimensions

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

Total New Old
Modular forms 200 48 152
Cusp forms 184 48 136
Eisenstein series 16 0 16

## Trace form

 $$48q + 8q^{3} - 48q^{4} - 8q^{9} + O(q^{10})$$ $$48q + 8q^{3} - 48q^{4} - 8q^{9} - 8q^{12} + 16q^{13} + 48q^{16} + 8q^{18} - 24q^{25} + 32q^{27} - 32q^{31} + 8q^{36} - 16q^{39} - 8q^{46} + 8q^{48} - 48q^{49} - 16q^{52} - 24q^{54} + 32q^{55} + 8q^{58} - 48q^{64} - 48q^{69} - 8q^{70} - 8q^{72} - 64q^{73} + 96q^{75} + 24q^{78} - 16q^{81} - 16q^{82} - 32q^{85} + 40q^{87} + 32q^{93} + 16q^{94} + O(q^{100})$$

## 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.h.a $$24$$ $$7.714$$ None $$0$$ $$4$$ $$-4$$ $$0$$
966.2.h.b $$24$$ $$7.714$$ None $$0$$ $$4$$ $$4$$ $$0$$

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

$$S_{2}^{\mathrm{old}}(966, [\chi]) \cong$$ $$S_{2}^{\mathrm{new}}(69, [\chi])$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(138, [\chi])$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(483, [\chi])$$$$^{\oplus 2}$$