Space of modular forms of level 24, weight 22, and trivial character

• Label: 24.22.a
• Level: $24$
• Weight: $22$
• Character orbit: 24.a
• Rep. character: $\chi_{24}(1,\cdot)$
• Character field: $\Q$
• Dimension: $11$
• Newform subspaces: $4$
• Sturm bound: $88$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	24.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(88\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_0(24))\).

	Total	New	Old
Modular forms	88	11	77
Cusp forms	80	11	69
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.
\(+\)	\(+\)	\(+\)	\(3\)
\(+\)	\(-\)	\(-\)	\(3\)
\(-\)	\(+\)	\(-\)	\(3\)
\(-\)	\(-\)	\(+\)	\(2\)
Plus space		\(+\)	\(5\)
Minus space		\(-\)	\(6\)

Trace form

\( 11 q - 59049 q^{3} + 24476018 q^{5} - 740760072 q^{7} + 38354628411 q^{9} + O(q^{10}) \)

Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_0(24))\) 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
24.22.a.a	$24$	$22$	24.a	1.a	$1$	$2$	$2$	$67.075$	\(\Q(\sqrt{537541}) \)	None	✓	$1$	$1$	\(0\)	\(118098\)	\(21948620\)	\(-659451408\)		$-$	$-$	$+$	$2^{7}\cdot 3^{2}\cdot 7$	$\mathrm{SU}(2)$	\(q+3^{10}q^{3}+(10974310-5\beta )q^{5}+(-329725704+\cdots)q^{7}+\cdots\)
24.22.a.b	$24$	$22$	24.a	1.a	$1$	$3$	$3$	$67.075$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(-177147\)	\(-4833126\)	\(271431024\)		$-$	$+$	$-$	$2^{21}\cdot 3^{4}\cdot 5\cdot 7$	$\mathrm{SU}(2)$	\(q-3^{10}q^{3}+(-1611042-\beta _{1})q^{5}+\cdots\)
24.22.a.c	$24$	$22$	24.a	1.a	$1$	$3$	$3$	$67.075$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$1$	\(0\)	\(-177147\)	\(2080026\)	\(-1205282064\)		$+$	$+$	$+$	$2^{21}\cdot 3^{4}\cdot 5\cdot 7$	$\mathrm{SU}(2)$	\(q-3^{10}q^{3}+(693342+\beta _{1})q^{5}+(-401760688+\cdots)q^{7}+\cdots\)
24.22.a.d	$24$	$22$	24.a	1.a	$1$	$3$	$3$	$67.075$	\(\mathbb{Q}[x]/(x^{3} - \cdots)\)	None	✓	$1$	$0$	\(0\)	\(177147\)	\(5280498\)	\(852542376\)		$+$	$-$	$-$	$2^{21}\cdot 3^{4}\cdot 7$	$\mathrm{SU}(2)$	\(q+3^{10}q^{3}+(1760166-\beta _{1})q^{5}+(284180792+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_0(24))\) into lower level spaces

\( S_{22}^{\mathrm{old}}(\Gamma_0(24)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 2}\)