Space of modular forms of level 24, weight 9, and Character 24.e

• Label: 24.9.e
• Level: $24$
• Weight: $9$
• Character orbit: 24.e
• Rep. character: $\chi_{24}(17,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	24.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(24, [\chi])\).

	Total	New	Old
Modular forms	36	8	28
Cusp forms	28	8	20
Eisenstein series	8	0	8

Trace form

8 * q + 56 * q^3 + 1584 * q^7 + 328 * q^9 + 25232 * q^13 + 38336 * q^15 + 157936 * q^19 + 30480 * q^21 - 579704 * q^25 - 276040 * q^27 + 805552 * q^31 + 102848 * q^33 - 3985008 * q^37 - 2297104 * q^39 + 6962672 * q^43 + 8670592 * q^45 - 5884520 * q^49 - 15590144 * q^51 + 27101312 * q^55 + 36756688 * q^57 - 51583600 * q^61 - 69759312 * q^63 + 58200688 * q^67 + 94226048 * q^69 - 116854768 * q^73 - 143181896 * q^75 + 172454576 * q^79 + 194700040 * q^81 - 264333824 * q^85 - 242851008 * q^87 + 382128480 * q^91 + 313470352 * q^93 - 337326704 * q^97 - 369701504 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(24, [\chi])\) 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				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
24.9.e.a	$24$	$9$	24.e	3.b	$2$	$8$	$8$	$9.777$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓	✓	✓	24.9.e.a	$2$	$0$	\(0\)	\(56\)	\(0\)	\(1584\)	$2^{42}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(7+\beta _{2})q^{3}+(-\beta _{2}+\beta _{4})q^{5}+(198+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(24, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(24, [\chi]) \simeq \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(6, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 2}\)