Properties

Label 24.4.a
Level $24$
Weight $4$
Character orbit 24.a
Rep. character $\chi_{24}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(24))\) into newform subspaces

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

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