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

• Label: 1156.1.m
• Level: $1156$
• Weight: $1$
• Character orbit: 1156.m
• Rep. character: $\chi_{1156}(35,\cdot)$
• Character field: $\Q(\zeta_{34})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $153$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1156 = 2^{2} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1156.m (of order \(34\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1156 \)
Character field:			\(\Q(\zeta_{34})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(153\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	48	48	0
Cusp forms	16	16	0
Eisenstein series	32	32	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

16 * q - q^2 - q^4 + 15 * q^5 - q^8 - q^9 - 2 * q^10 - 2 * q^13 - q^16 - q^17 - q^18 - 2 * q^20 + 14 * q^25 - 2 * q^26 - 2 * q^29 - q^32 - q^34 - q^36 - 2 * q^37 - 2 * q^40 - 2 * q^41 - 2 * q^45 - q^49 - 3 * q^50 + 15 * q^52 - 2 * q^53 - 2 * q^58 - 2 * q^61 - q^64 - 4 * q^65 - q^68 - q^72 - 2 * q^73 - 2 * q^74 - 2 * q^80 - q^81 - 2 * q^82 - 2 * q^85 - 2 * q^89 - 2 * q^90 - 2 * q^97 - q^98

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.m.a	$1156$	$1$	1156.m	1156.m	$34$	$16$	$1$	$0.577$	\(\Q(\zeta_{34})\)	$D_{17}$	\(\Q(\sqrt{-1}) \)	None		✓	✓	✓	1156.1.m.a	$4$	$0$	\(-1\)	\(0\)	\(15\)	\(0\)	$1$		\(q+\zeta_{34}^{6}q^{2}+\zeta_{34}^{12}q^{4}+(1-\zeta_{34}^{15}+\cdots)q^{5}+\cdots\)