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 $0$

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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

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

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

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