Space of modular forms of level 1176, weight 3, and Character 1176.f

• Label: 1176.3.f
• Level: $1176$
• Weight: $3$
• Character orbit: 1176.f
• Rep. character: $\chi_{1176}(97,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $4$
• Sturm bound: $672$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1176.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(672\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1176, [\chi])\).

	Total	New	Old
Modular forms	480	40	440
Cusp forms	416	40	376
Eisenstein series	64	0	64

Trace form

40 * q - 120 * q^9 + 16 * q^11 - 24 * q^15 - 96 * q^23 - 256 * q^25 + 64 * q^29 + 8 * q^37 + 48 * q^39 - 144 * q^43 + 48 * q^51 + 48 * q^53 + 120 * q^57 + 528 * q^65 + 48 * q^67 - 32 * q^71 - 56 * q^79 + 360 * q^81 - 96 * q^85 - 216 * q^93 + 416 * q^95 - 48 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(1176, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1176.3.f.a	$1176$	$3$	1176.f	7.b	$2$	$8$	$8$	$32.044$	8.0.\(\cdots\).2	None					168.3.z.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{3}+(-\beta _{2}-\beta _{5})q^{5}-3q^{9}+(-3+\cdots)q^{11}+\cdots\)
1176.3.f.b	$1176$	$3$	1176.f	7.b	$2$	$8$	$8$	$32.044$	8.0.339738624.1	None		✓			1176.3.f.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{3}+(2\beta _{2}-\beta _{5}-\beta _{7})q^{5}-3q^{9}+\cdots\)
1176.3.f.c	$1176$	$3$	1176.f	7.b	$2$	$8$	$8$	$32.044$	8.0.\(\cdots\).9	None					168.3.z.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{7})q^{5}-3q^{9}+(5+\beta _{2}+\cdots)q^{11}+\cdots\)
1176.3.f.d	$1176$	$3$	1176.f	7.b	$2$	$16$	$16$	$32.044$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		1176.3.f.d	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}\cdot 7^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+(-\beta _{2}+\beta _{11})q^{5}-3q^{9}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(1176, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1176, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(392, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)