Space of modular forms of level 24, weight 10, and trivial character

• Label: 24.10.a
• Level: $24$
• Weight: $10$
• Character orbit: 24.a
• Rep. character: $\chi_{24}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $4$
• Sturm bound: $40$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	24.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(40\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(24))\).

	Total	New	Old
Modular forms	40	5	35
Cusp forms	32	5	27
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
\(+\)	\(+\)	$+$	\(1\)
\(+\)	\(-\)	$-$	\(1\)
\(-\)	\(+\)	$-$	\(2\)
\(-\)	\(-\)	$+$	\(1\)
Plus space		\(+\)	\(2\)
Minus space		\(-\)	\(3\)

Trace form

\( 5 q - 81 q^{3} - 122 q^{5} - 5904 q^{7} + 32805 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(24))\) 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
24.10.a.a	$24$	$10$	24.a	1.a	$1$	$1$	$1$	$12.361$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-81\)	\(830\)	\(672\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3^{4}q^{3}+830q^{5}+672q^{7}+3^{8}q^{9}+\cdots\)
24.10.a.b	$24$	$10$	24.a	1.a	$1$	$1$	$1$	$12.361$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(81\)	\(-794\)	\(-5880\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3^{4}q^{3}-794q^{5}-5880q^{7}+3^{8}q^{9}+\cdots\)
24.10.a.c	$24$	$10$	24.a	1.a	$1$	$1$	$1$	$12.361$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(81\)	\(614\)	\(2184\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3^{4}q^{3}+614q^{5}+2184q^{7}+3^{8}q^{9}+\cdots\)
24.10.a.d	$24$	$10$	24.a	1.a	$1$	$2$	$2$	$12.361$	\(\Q(\sqrt{109}) \)	None	✓	$1$	$0$	\(0\)	\(-162\)	\(-772\)	\(-2880\)		$-$	$+$	$-$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q-3^{4}q^{3}+(-386-\beta )q^{5}+(-1440+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(24))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(24)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 2}\)