Properties

Label 24.2.f
Level $24$
Weight $2$
Character orbit 24.f
Rep. character $\chi_{24}(11,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $8$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 24.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 24 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(24, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

Trace form

\( 2q - 2q^{3} - 4q^{4} + 4q^{6} - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{3} - 4q^{4} + 4q^{6} - 2q^{9} + 4q^{12} + 8q^{16} - 8q^{18} + 4q^{19} - 8q^{22} - 8q^{24} - 10q^{25} + 10q^{27} + 8q^{33} + 16q^{34} + 4q^{36} - 20q^{43} - 8q^{48} + 14q^{49} - 16q^{51} + 4q^{54} - 4q^{57} - 16q^{64} + 8q^{66} + 28q^{67} + 16q^{72} + 4q^{73} + 10q^{75} - 8q^{76} - 14q^{81} - 32q^{82} + 16q^{88} + 16q^{96} - 20q^{97} - 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(24, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
24.2.f.a \(2\) \(0.192\) \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) \(0\) \(-2\) \(0\) \(0\) \(q+\beta q^{2}+(-1-\beta )q^{3}-2q^{4}+(2-\beta )q^{6}+\cdots\)