Space of modular forms of level 24, weight 8, and trivial character

• Label: 24.8.a
• Level: $24$
• Weight: $8$
• Character orbit: 24.a
• Rep. character: $\chi_{24}(1,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $3$
• Sturm bound: $32$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	24.a (trivial)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(32\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(24))\).

	Total	New	Old
Modular forms	32	3	29
Cusp forms	24	3	21
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		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(9\)	\(1\)	\(8\)		\(7\)	\(1\)	\(6\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)		\(8\)	\(1\)	\(7\)		\(6\)	\(1\)	\(5\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(7\)	\(0\)	\(7\)		\(5\)	\(0\)	\(5\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)		\(8\)	\(1\)	\(7\)		\(6\)	\(1\)	\(5\)		\(2\)	\(0\)	\(2\)
Plus space		\(+\)		\(17\)	\(2\)	\(15\)		\(13\)	\(2\)	\(11\)		\(4\)	\(0\)	\(4\)
Minus space		\(-\)		\(15\)	\(1\)	\(14\)		\(11\)	\(1\)	\(10\)		\(4\)	\(0\)	\(4\)

Trace form

3 * q + 27 * q^3 - 446 * q^5 + 1680 * q^7 + 2187 * q^9 + 3028 * q^11 + 5154 * q^13 - 10638 * q^15 + 38534 * q^17 + 10188 * q^19 - 11664 * q^21 - 164264 * q^23 + 59301 * q^25 + 19683 * q^27 - 106902 * q^29 - 2472 * q^31 - 264492 * q^33 - 35616 * q^35 + 469002 * q^37 - 141966 * q^39 + 883998 * q^41 + 1002132 * q^43 - 325134 * q^45 - 1575840 * q^47 - 1087077 * q^49 + 1377270 * q^51 + 455554 * q^53 + 4066488 * q^55 - 1965492 * q^57 - 2921612 * q^59 - 5417118 * q^61 + 1224720 * q^63 + 6019564 * q^65 - 5075988 * q^67 - 2845800 * q^69 - 3629080 * q^71 + 1953390 * q^73 + 5783373 * q^75 + 7828800 * q^77 + 2669064 * q^79 + 1594323 * q^81 - 11429812 * q^83 - 6864252 * q^85 + 8480538 * q^87 + 17086494 * q^89 + 9167712 * q^91 - 10069704 * q^93 - 9004792 * q^95 - 9134586 * q^97 + 2207412 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(24))\) 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
24.8.a.a	$24$	$8$	24.a	1.a	$1$	$1$	$1$	$7.497$	\(\Q\)	None	✓	✓	✓	✓	24.8.a.a	$1$	$0$	\(0\)	\(-27\)	\(-26\)	\(1056\)		$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	\(q-3^{3}q^{3}-26q^{5}+1056q^{7}+3^{6}q^{9}+\cdots\)
24.8.a.b	$24$	$8$	24.a	1.a	$1$	$1$	$1$	$7.497$	\(\Q\)	None	✓	✓	✓	✓	24.8.a.b	$1$	$1$	\(0\)	\(27\)	\(-530\)	\(120\)		$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	\(q+3^{3}q^{3}-530q^{5}+120q^{7}+3^{6}q^{9}+\cdots\)
24.8.a.c	$24$	$8$	24.a	1.a	$1$	$1$	$1$	$7.497$	\(\Q\)	None	✓	✓	✓	✓	24.8.a.c	$1$	$0$	\(0\)	\(27\)	\(110\)	\(504\)		$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	\(q+3^{3}q^{3}+110q^{5}+504q^{7}+3^{6}q^{9}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(24))\) into lower level spaces

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