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		Total				Cusp				Eisenstein
				All	New	Old		All	New	Old		All	New	Old
\(+\)	\(+\)	\(+\)		\(9\)	\(1\)	\(8\)		\(7\)	\(1\)	\(6\)		\(2\)	\(0\)	\(2\)
\(+\)	\(-\)	\(-\)		\(10\)	\(1\)	\(9\)		\(8\)	\(1\)	\(7\)		\(2\)	\(0\)	\(2\)
\(-\)	\(+\)	\(-\)		\(11\)	\(2\)	\(9\)		\(9\)	\(2\)	\(7\)		\(2\)	\(0\)	\(2\)
\(-\)	\(-\)	\(+\)		\(10\)	\(1\)	\(9\)		\(8\)	\(1\)	\(7\)		\(2\)	\(0\)	\(2\)
Plus space		\(+\)		\(19\)	\(2\)	\(17\)		\(15\)	\(2\)	\(13\)		\(4\)	\(0\)	\(4\)
Minus space		\(-\)		\(21\)	\(3\)	\(18\)		\(17\)	\(3\)	\(14\)		\(4\)	\(0\)	\(4\)

Trace form

5 * q - 81 * q^3 - 122 * q^5 - 5904 * q^7 + 32805 * q^9 - 56924 * q^11 + 253814 * q^13 - 19278 * q^15 + 371690 * q^17 + 166300 * q^19 - 120528 * q^21 + 2393560 * q^23 + 265051 * q^25 - 531441 * q^27 - 736818 * q^29 + 56248 * q^31 + 446796 * q^33 - 32502624 * q^35 + 21407934 * q^37 - 11710494 * q^39 + 3652674 * q^41 - 38861212 * q^43 - 800442 * q^45 + 77893536 * q^47 + 43083805 * q^49 - 62200386 * q^51 - 122788058 * q^53 + 191168888 * q^55 + 12974580 * q^57 + 35469124 * q^59 + 203888918 * q^61 - 38736144 * q^63 - 197295884 * q^65 - 183464900 * q^67 + 163576584 * q^69 + 334361960 * q^71 + 307233266 * q^73 - 491077647 * q^75 - 1124684736 * q^77 - 598882456 * q^79 + 215233605 * q^81 + 1832558108 * q^83 - 291062708 * q^85 - 837938358 * q^87 - 1995331614 * q^89 + 192513312 * q^91 + 1493236296 * q^93 + 2022308360 * q^95 + 1970064970 * q^97 - 373478364 * q^99

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

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

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