Properties

Label 24.4.a
Level 24
Weight 4
Character orbit a
Rep. character \(\chi_{24}(1,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 16
Trace bound 0

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Defining parameters

Level: \( N \) = \( 24 = 2^{3} \cdot 3 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 24.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(16\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(24))\).

Total New Old
Modular forms 16 1 15
Cusp forms 8 1 7
Eisenstein series 8 0 8

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\(+\)\(1\)
Minus space\(-\)\(0\)

Trace form

\(q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 14q^{5} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 14q^{5} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut -\mathstrut 28q^{11} \) \(\mathstrut -\mathstrut 74q^{13} \) \(\mathstrut +\mathstrut 42q^{15} \) \(\mathstrut +\mathstrut 82q^{17} \) \(\mathstrut +\mathstrut 92q^{19} \) \(\mathstrut -\mathstrut 72q^{21} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut +\mathstrut 71q^{25} \) \(\mathstrut +\mathstrut 27q^{27} \) \(\mathstrut -\mathstrut 138q^{29} \) \(\mathstrut +\mathstrut 80q^{31} \) \(\mathstrut -\mathstrut 84q^{33} \) \(\mathstrut -\mathstrut 336q^{35} \) \(\mathstrut +\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 222q^{39} \) \(\mathstrut +\mathstrut 282q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 126q^{45} \) \(\mathstrut +\mathstrut 240q^{47} \) \(\mathstrut +\mathstrut 233q^{49} \) \(\mathstrut +\mathstrut 246q^{51} \) \(\mathstrut -\mathstrut 130q^{53} \) \(\mathstrut -\mathstrut 392q^{55} \) \(\mathstrut +\mathstrut 276q^{57} \) \(\mathstrut +\mathstrut 596q^{59} \) \(\mathstrut -\mathstrut 218q^{61} \) \(\mathstrut -\mathstrut 216q^{63} \) \(\mathstrut -\mathstrut 1036q^{65} \) \(\mathstrut -\mathstrut 436q^{67} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 856q^{71} \) \(\mathstrut -\mathstrut 998q^{73} \) \(\mathstrut +\mathstrut 213q^{75} \) \(\mathstrut +\mathstrut 672q^{77} \) \(\mathstrut -\mathstrut 32q^{79} \) \(\mathstrut +\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 1508q^{83} \) \(\mathstrut +\mathstrut 1148q^{85} \) \(\mathstrut -\mathstrut 414q^{87} \) \(\mathstrut -\mathstrut 246q^{89} \) \(\mathstrut +\mathstrut 1776q^{91} \) \(\mathstrut +\mathstrut 240q^{93} \) \(\mathstrut +\mathstrut 1288q^{95} \) \(\mathstrut +\mathstrut 866q^{97} \) \(\mathstrut -\mathstrut 252q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(24))\) 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
24.4.a.a \(1\) \(1.416\) \(\Q\) None \(0\) \(3\) \(14\) \(-24\) \(-\) \(-\) \(q+3q^{3}+14q^{5}-24q^{7}+9q^{9}-28q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(24))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(24)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 2}\)