Space of modular forms of level 24, weight 2, and trivial character

• Label: 24.2.a
• Level: $24$
• Weight: $2$
• Character orbit: 24.a
• Rep. character: $\chi_{24}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $8$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	24.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(8\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(24))\).

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

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		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(1\)	\(0\)	\(1\)		\(0\)	\(0\)	\(0\)		\(1\)	\(0\)	\(1\)
\(+\)	\(-\)	\(-\)		\(2\)	\(0\)	\(2\)		\(0\)	\(0\)	\(0\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(3\)	\(1\)	\(2\)		\(1\)	\(1\)	\(0\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)		\(2\)	\(0\)	\(2\)		\(0\)	\(0\)	\(0\)		\(2\)	\(0\)	\(2\)
Plus space		\(+\)		\(3\)	\(0\)	\(3\)		\(0\)	\(0\)	\(0\)		\(3\)	\(0\)	\(3\)
Minus space		\(-\)		\(5\)	\(1\)	\(4\)		\(1\)	\(1\)	\(0\)		\(4\)	\(0\)	\(4\)

Trace form

q - q^3 - 2 * q^5 + q^9 + 4 * q^11 - 2 * q^13 + 2 * q^15 + 2 * q^17 - 4 * q^19 - 8 * q^23 - q^25 - q^27 + 6 * q^29 + 8 * q^31 - 4 * q^33 + 6 * q^37 + 2 * q^39 - 6 * q^41 + 4 * q^43 - 2 * q^45 - 7 * q^49 - 2 * q^51 - 2 * q^53 - 8 * q^55 + 4 * q^57 + 4 * q^59 - 2 * q^61 + 4 * q^65 - 4 * q^67 + 8 * q^69 + 8 * q^71 + 10 * q^73 + q^75 - 8 * q^79 + q^81 - 4 * q^83 - 4 * q^85 - 6 * q^87 - 6 * q^89 - 8 * q^93 + 8 * q^95 + 2 * q^97 + 4 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(24))\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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
24.2.a.a	$24$	$2$	24.a	1.a	$1$	$1$	$1$	$0.192$	\(\Q\)	None	✓	✓	✓	✓	24.2.a.a	$1$	$0$	\(0\)	\(-1\)	\(-2\)	\(0\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-q^{3}-2q^{5}+q^{9}+4q^{11}-2q^{13}+\cdots\)