Space of modular forms of level 1156, weight 1, and Character 1156.f

• Label: 1156.1.f
• Level: $1156$
• Weight: $1$
• Character orbit: 1156.f
• Rep. character: $\chi_{1156}(251,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $2$
• Sturm bound: $153$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1156 = 2^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1156.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 68 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(153\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1156, [\chi])\).

	Total	New	Old
Modular forms	44	32	12
Cusp forms	8	4	4
Eisenstein series	36	28	8

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

\( 4 q - 4 q^{4} + 2 q^{5} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1156, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1156.1.f.a	$1156$	$1$	1156.f	68.f	$4$	$2$	$1$	$0.577$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \)	\(\Q(\sqrt{17}) \)					68.1.d.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+iq^{2}-q^{4}-iq^{8}-iq^{9}+q^{13}+\cdots\)
1156.1.f.b	$1156$	$1$	1156.f	68.f	$4$	$2$	$1$	$0.577$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None					68.1.f.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q-iq^{2}-q^{4}+(1-i)q^{5}+iq^{8}-iq^{9}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1156, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1156, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(68, [\chi])\)\(^{\oplus 2}\)