Properties

Label 24.2.a
Level 24
Weight 2
Character orbit a
Rep. character \(\chi_{24}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 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: \(\Q\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 3
24.2.a.a \(1\) \(0.192\) \(\Q\) None \(0\) \(-1\) \(-2\) \(0\) \(-\) \(+\) \(q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)