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

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

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 3
24.4.a.a 24.a 1.a $1$ $1.416$ \(\Q\) None 24.4.a.a \(0\) \(3\) \(14\) \(-24\) $-$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+14q^{5}-24q^{7}+9q^{9}-28q^{11}+\cdots\)

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

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