Space of modular forms of level 3, weight 24, and trivial character

• Label: 3.24.a
• Level: $3$
• Weight: $24$
• Character orbit: 3.a
• Rep. character: $\chi_{3}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $8$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(8\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{24}(\Gamma_0(3))\).

	Total	New	Old
Modular forms	9	3	6
Cusp forms	7	3	4
Eisenstein series	2	0	2

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)	Dim
\(+\)	\(2\)
\(-\)	\(1\)

Trace form

\( 3 q - 114 q^{2} - 177147 q^{3} - 13574940 q^{4} - 95672550 q^{5} + 419838390 q^{6} - 1935652584 q^{7} - 14917581480 q^{8} + 94143178827 q^{9} + O(q^{10}) \)

Decomposition of \(S_{24}^{\mathrm{new}}(\Gamma_0(3))\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$		3
3.24.a.a	$3$	$24$	3.a	1.a	$1$	$1$	$1$	$10.056$	\(\Q\)	None	✓	$1$	$1$	\(1128\)	\(177147\)	\(-48863730\)	\(-1723688680\)		$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+1128q^{2}+3^{11}q^{3}-7116224q^{4}+\cdots\)
3.24.a.b	$3$	$24$	3.a	1.a	$1$	$2$	$2$	$10.056$	\(\Q(\sqrt{530401}) \)	None	✓	$1$	$0$	\(-1242\)	\(-354294\)	\(-46808820\)	\(-211963904\)		$+$	$+$	$2\cdot 3$	$\mathrm{SU}(2)$	\(q+(-621-\beta )q^{2}-3^{11}q^{3}+(-3229358+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{24}^{\mathrm{old}}(\Gamma_0(3))\) into lower level spaces

\( S_{24}^{\mathrm{old}}(\Gamma_0(3)) \cong \) \(S_{24}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)