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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

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
24.3.e.a 24.e 3.b $2$ $0.654$ \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta )q^{3}-2\beta q^{5}-6q^{7}+(-7+2\beta )q^{9}+\cdots\)

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

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