# Properties

 Label 24.3.h Level $24$ Weight $3$ Character orbit 24.h Rep. character $\chi_{24}(5,\cdot)$ Character field $\Q$ Dimension $6$ Newform subspaces $3$ Sturm bound $12$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$24 = 2^{3} \cdot 3$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 24.h (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$24$$ Character field: $$\Q$$ Newform subspaces: $$3$$ Sturm bound: $$12$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$5$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(24, [\chi])$$.

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

## Trace form

 $$6q - 4q^{4} - 8q^{6} - 4q^{7} - 2q^{9} + O(q^{10})$$ $$6q - 4q^{4} - 8q^{6} - 4q^{7} - 2q^{9} - 24q^{10} + 28q^{12} - 20q^{15} + 40q^{16} + 56q^{18} + 64q^{22} - 88q^{24} - 14q^{25} - 128q^{28} - 112q^{30} + 60q^{31} - 12q^{33} - 112q^{34} + 132q^{36} + 112q^{39} + 128q^{40} + 136q^{42} + 224q^{46} - 168q^{48} - 30q^{49} - 112q^{52} - 184q^{54} - 232q^{55} + 56q^{57} - 152q^{58} + 144q^{60} - 260q^{63} + 272q^{64} + 168q^{66} + 16q^{70} - 112q^{72} + 76q^{73} - 56q^{76} - 112q^{78} + 380q^{79} + 38q^{81} - 224q^{82} + 112q^{84} + 396q^{87} - 80q^{88} + 8q^{90} - 16q^{96} + 92q^{97} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(24, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
24.3.h.a $$1$$ $$0.654$$ $$\Q$$ $$\Q(\sqrt{-6})$$ $$-2$$ $$3$$ $$2$$ $$-10$$ $$q-2q^{2}+3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots$$
24.3.h.b $$1$$ $$0.654$$ $$\Q$$ $$\Q(\sqrt{-6})$$ $$2$$ $$-3$$ $$-2$$ $$-10$$ $$q+2q^{2}-3q^{3}+4q^{4}-2q^{5}-6q^{6}+\cdots$$
24.3.h.c $$4$$ $$0.654$$ $$\Q(\sqrt{2}, \sqrt{-7})$$ None $$0$$ $$0$$ $$0$$ $$16$$ $$q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(-3+\beta _{3})q^{4}+\cdots$$