Space of modular forms of level 24, weight 26, and trivial character

• Label: 24.26.a
• Level: $24$
• Weight: $26$
• Character orbit: 24.a
• Rep. character: $\chi_{24}(1,\cdot)$
• Character field: $\Q$
• Dimension: $13$
• Newform subspaces: $4$
• Sturm bound: $104$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	24.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(104\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_0(24))\).

	Total	New	Old
Modular forms	104	13	91
Cusp forms	96	13	83
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
\(+\)	\(+\)	$+$	\(3\)
\(+\)	\(-\)	$-$	\(3\)
\(-\)	\(+\)	$-$	\(4\)
\(-\)	\(-\)	$+$	\(3\)
Plus space		\(+\)	\(6\)
Minus space		\(-\)	\(7\)

Trace form

\( 13 q - 531441 q^{3} - 911313002 q^{5} + 6873090000 q^{7} + 3671583974253 q^{9} + O(q^{10}) \)

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_0(24))\) 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
24.26.a.a	$24$	$26$	24.a	1.a	$1$	$3$	$3$	$95.039$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-1594323\)	\(-341050950\)	\(-1095757536\)		$+$	$+$	$+$	$2^{22}\cdot 3^{5}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q-3^{12}q^{3}+(-113683650+\beta _{1})q^{5}+\cdots\)
24.26.a.b	$24$	$26$	24.a	1.a	$1$	$3$	$3$	$95.039$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(1594323\)	\(-560960334\)	\(27161710296\)		$-$	$-$	$+$	$2^{21}\cdot 3^{4}\cdot 5$	$\mathrm{SU}(2)$	\(q+3^{12}q^{3}+(-186986778-\beta _{2})q^{5}+\cdots\)
24.26.a.c	$24$	$26$	24.a	1.a	$1$	$3$	$3$	$95.039$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(1594323\)	\(-275737806\)	\(-19677447336\)		$+$	$-$	$-$	$2^{21}\cdot 3^{4}\cdot 5$	$\mathrm{SU}(2)$	\(q+3^{12}q^{3}+(-91912602-\beta _{1})q^{5}+\cdots\)
24.26.a.d	$24$	$26$	24.a	1.a	$1$	$4$	$4$	$95.039$	\(\mathbb{Q}[x]/(x^{4} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-2125764\)	\(266436088\)	\(484584576\)		$-$	$+$	$-$	$2^{42}\cdot 3^{8}\cdot 5^{2}$	$\mathrm{SU}(2)$	\(q-3^{12}q^{3}+(66609022+\beta _{1})q^{5}+(121146144+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_0(24))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_0(24)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 2}\)