Space of modular forms of level 24, weight 12, and trivial character

• Label: 24.12.a
• Level: $24$
• Weight: $12$
• Character orbit: 24.a
• Rep. character: $\chi_{24}(1,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $4$
• Sturm bound: $48$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	24.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(48\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(24))\).

	Total	New	Old
Modular forms	48	5	43
Cusp forms	40	5	35
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
\(+\)	\(+\)	$+$	\(1\)
\(+\)	\(-\)	$-$	\(1\)
\(-\)	\(+\)	$-$	\(1\)
\(-\)	\(-\)	$+$	\(2\)
Plus space		\(+\)	\(3\)
Minus space		\(-\)	\(2\)

Trace form

\( 5 q + 243 q^{3} - 2506 q^{5} - 35592 q^{7} + 295245 q^{9} + O(q^{10}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(24))\) 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
24.12.a.a	$24$	$12$	24.a	1.a	$1$	$1$	$1$	$18.440$	\(\Q\)	None	✓	$1$	$0$	\(0\)	\(-243\)	\(-7130\)	\(-19536\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3^{5}q^{3}-7130q^{5}-19536q^{7}+3^{10}q^{9}+\cdots\)
24.12.a.b	$24$	$12$	24.a	1.a	$1$	$1$	$1$	$18.440$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(-243\)	\(1190\)	\(18480\)		$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	\(q-3^{5}q^{3}+1190q^{5}+18480q^{7}+3^{10}q^{9}+\cdots\)
24.12.a.c	$24$	$12$	24.a	1.a	$1$	$1$	$1$	$18.440$	\(\Q\)	None	✓	$1$	$1$	\(0\)	\(243\)	\(1870\)	\(-72312\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3^{5}q^{3}+1870q^{5}-72312q^{7}+3^{10}q^{9}+\cdots\)
24.12.a.d	$24$	$12$	24.a	1.a	$1$	$2$	$2$	$18.440$	\(\Q(\sqrt{3061}) \)	None	✓	$1$	$0$	\(0\)	\(486\)	\(1564\)	\(37776\)		$-$	$-$	$+$	$2^{7}\cdot 3$	$\mathrm{SU}(2)$	\(q+3^{5}q^{3}+(782-\beta )q^{5}+(18888+\beta )q^{7}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(24))\) into lower level spaces

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