Space of modular forms of level 24, weight 3, and Character 24.h

• Label: 24.3.h
• Level: $24$
• Weight: $3$
• Character orbit: 24.h
• Rep. character: $\chi_{24}(5,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $12$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	24.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(12\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(24, [\chi])\).

	Total	New	Old
Modular forms	10	10	0
Cusp forms	6	6	0
Eisenstein series	4	4	0

Trace form

6 * q - 4 * q^4 - 8 * q^6 - 4 * q^7 - 2 * q^9 - 24 * q^10 + 28 * q^12 - 20 * q^15 + 40 * q^16 + 56 * q^18 + 64 * q^22 - 88 * q^24 - 14 * q^25 - 128 * q^28 - 112 * q^30 + 60 * q^31 - 12 * q^33 - 112 * q^34 + 132 * q^36 + 112 * q^39 + 128 * q^40 + 136 * q^42 + 224 * q^46 - 168 * q^48 - 30 * q^49 - 112 * q^52 - 184 * q^54 - 232 * q^55 + 56 * q^57 - 152 * q^58 + 144 * q^60 - 260 * q^63 + 272 * q^64 + 168 * q^66 + 16 * q^70 - 112 * q^72 + 76 * q^73 - 56 * q^76 - 112 * q^78 + 380 * q^79 + 38 * q^81 - 224 * q^82 + 112 * q^84 + 396 * q^87 - 80 * q^88 + 8 * q^90 - 16 * q^96 + 92 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(24, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
24.3.h.a	$24$	$3$	24.h	24.h	$2$	$1$	$1$	$0.654$	\(\Q\)	\(\Q(\sqrt{-6}) \)	✓	✓			24.3.h.a	$2$	$0$	\(-2\)	\(3\)	\(2\)	\(-10\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-2q^{2}+3q^{3}+4q^{4}+2q^{5}-6q^{6}+\cdots\)
24.3.h.b	$24$	$3$	24.h	24.h	$2$	$1$	$1$	$0.654$	\(\Q\)	\(\Q(\sqrt{-6}) \)	✓	✓			24.3.h.a	$2$	$0$	\(2\)	\(-3\)	\(-2\)	\(-10\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2q^{2}-3q^{3}+4q^{4}-2q^{5}-6q^{6}+\cdots\)
24.3.h.c	$24$	$3$	24.h	24.h	$2$	$4$	$4$	$0.654$	\(\Q(\sqrt{2}, \sqrt{-7})\)	None		✓	✓		24.3.h.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(-3+\beta _{3})q^{4}+\cdots\)