Space of modular forms of level 24, weight 4, and trivial character

• Label: 24.4.a
• Level: $24$
• Weight: $4$
• Character orbit: 24.a
• Rep. character: $\chi_{24}(1,\cdot)$
• Character field: $\Q$
• Dimension: $1$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	24.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(16\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(24))\).

	Total	New	Old
Modular forms	16	1	15
Cusp forms	8	1	7
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
\(-\)	\(-\)	\(+\)	\(1\)
Plus space		\(+\)	\(1\)
Minus space		\(-\)	\(0\)

Trace form

q + 3 * q^3 + 14 * q^5 - 24 * q^7 + 9 * q^9 - 28 * q^11 - 74 * q^13 + 42 * q^15 + 82 * q^17 + 92 * q^19 - 72 * q^21 + 8 * q^23 + 71 * q^25 + 27 * q^27 - 138 * q^29 + 80 * q^31 - 84 * q^33 - 336 * q^35 + 30 * q^37 - 222 * q^39 + 282 * q^41 + 4 * q^43 + 126 * q^45 + 240 * q^47 + 233 * q^49 + 246 * q^51 - 130 * q^53 - 392 * q^55 + 276 * q^57 + 596 * q^59 - 218 * q^61 - 216 * q^63 - 1036 * q^65 - 436 * q^67 + 24 * q^69 + 856 * q^71 - 998 * q^73 + 213 * q^75 + 672 * q^77 - 32 * q^79 + 81 * q^81 - 1508 * q^83 + 1148 * q^85 - 414 * q^87 - 246 * q^89 + 1776 * q^91 + 240 * q^93 + 1288 * q^95 + 866 * q^97 - 252 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(24))\) 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
24.4.a.a	$24$	$4$	24.a	1.a	$1$	$1$	$1$	$1.416$	\(\Q\)	None	✓	✓	✓	✓	24.4.a.a	$1$	$0$	\(0\)	\(3\)	\(14\)	\(-24\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3q^{3}+14q^{5}-24q^{7}+9q^{9}-28q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(24))\) into lower level spaces

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