Space of modular forms of level 24, weight 4, and trivial character

• 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: $0$

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.

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

Trace form

\( q + 3 q^{3} + 14 q^{5} - 24 q^{7} + 9 q^{9} + O(q^{10}) \)

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces					A-L signs		Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		2	3
24.4.a.a	$24$	$4$	24.a	1.a	$1$	$1$	$1$	$1.416$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(3\)	\(14\)	\(-24\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+14q^{5}-24q^{7}+9q^{9}-28q^{11}+\cdots\)

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

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