Properties

 Label 24.3.e Level $24$ Weight $3$ Character orbit 24.e Rep. character $\chi_{24}(17,\cdot)$ Character field $\Q$ Dimension $2$ Newform subspaces $1$ Sturm bound $12$ Trace bound $0$

Related objects

Defining parameters

 Level: $$N$$ $$=$$ $$24 = 2^{3} \cdot 3$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 24.e (of order $$2$$ and degree $$1$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$3$$ Character field: $$\Q$$ Newform subspaces: $$1$$ Sturm bound: $$12$$ Trace bound: $$0$$

Dimensions

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

Total New Old
Modular forms 12 2 10
Cusp forms 4 2 2
Eisenstein series 8 0 8

Trace form

 $$2 q + 2 q^{3} - 12 q^{7} - 14 q^{9} + O(q^{10})$$ $$2 q + 2 q^{3} - 12 q^{7} - 14 q^{9} + 20 q^{13} + 32 q^{15} + 4 q^{19} - 12 q^{21} - 14 q^{25} - 46 q^{27} - 44 q^{31} + 32 q^{33} - 12 q^{37} + 20 q^{39} + 164 q^{43} + 64 q^{45} - 26 q^{49} - 128 q^{51} - 64 q^{55} + 4 q^{57} - 172 q^{61} + 84 q^{63} + 4 q^{67} - 64 q^{69} + 164 q^{73} - 14 q^{75} + 20 q^{79} + 34 q^{81} + 256 q^{85} + 96 q^{87} - 120 q^{91} - 44 q^{93} - 188 q^{97} + 64 q^{99} + O(q^{100})$$

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.e.a $2$ $0.654$ $$\Q(\sqrt{-2})$$ None $$0$$ $$2$$ $$0$$ $$-12$$ $$q+(1+\beta )q^{3}-2\beta q^{5}-6q^{7}+(-7+2\beta )q^{9}+\cdots$$

Decomposition of $$S_{3}^{\mathrm{old}}(24, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(24, [\chi]) \simeq$$ $$S_{3}^{\mathrm{new}}(12, [\chi])$$$$^{\oplus 2}$$