Properties

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(24))\).

Total New Old
Modular forms 8 1 7
Cusp forms 1 1 0
Eisenstein series 7 0 7

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(3\)FrickeDim
\(-\)\(+\)$-$\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(1\)

Trace form

\( q - q^{3} - 2 q^{5} + q^{9} + O(q^{10}) \) \( q - q^{3} - 2 q^{5} + q^{9} + 4 q^{11} - 2 q^{13} + 2 q^{15} + 2 q^{17} - 4 q^{19} - 8 q^{23} - q^{25} - q^{27} + 6 q^{29} + 8 q^{31} - 4 q^{33} + 6 q^{37} + 2 q^{39} - 6 q^{41} + 4 q^{43} - 2 q^{45} - 7 q^{49} - 2 q^{51} - 2 q^{53} - 8 q^{55} + 4 q^{57} + 4 q^{59} - 2 q^{61} + 4 q^{65} - 4 q^{67} + 8 q^{69} + 8 q^{71} + 10 q^{73} + q^{75} - 8 q^{79} + q^{81} - 4 q^{83} - 4 q^{85} - 6 q^{87} - 6 q^{89} - 8 q^{93} + 8 q^{95} + 2 q^{97} + 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
24.2.a.a 24.a 1.a $1$ $0.192$ \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)