Space of modular forms of level 1176, weight 2, and Character 1176.k

• Label: 1176.2.k
• Level: $1176$
• Weight: $2$
• Character orbit: 1176.k
• Rep. character: $\chi_{1176}(881,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $2$
• Sturm bound: $448$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1176.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(448\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1176, [\chi])\).

	Total	New	Old
Modular forms	256	40	216
Cusp forms	192	40	152
Eisenstein series	64	0	64

Trace form

\( 40 q - 4 q^{9} - 8 q^{15} + 44 q^{25} + 20 q^{37} - 20 q^{39} + 36 q^{43} + 36 q^{51} + 40 q^{57} - 12 q^{67} - 56 q^{79} + 20 q^{81} - 48 q^{85} - 64 q^{93} - 36 q^{99}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1176, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1176.2.k.a	$1176$	$2$	1176.k	21.c	$2$	$16$	$16$	$9.390$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None					168.2.u.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{8}q^{5}+\beta _{5}q^{9}-\beta _{6}q^{11}+\cdots\)
1176.2.k.b	$1176$	$2$	1176.k	21.c	$2$	$24$	$24$	$9.390$		None		✓	✓		1176.2.k.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1176, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1176, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(147, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(294, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(588, [\chi])\)\(^{\oplus 2}\)