Space of modular forms of level 187, weight 2, and Character 187.m

• Label: 187.2.m
• Level: $187$
• Weight: $2$
• Character orbit: 187.m
• Rep. character: $\chi_{187}(10,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $128$
• Newform subspaces: $1$
• Sturm bound: $36$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 187 = 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	187.m (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 187 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(36\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(187, [\chi])\).

	Total	New	Old
Modular forms	160	160	0
Cusp forms	128	128	0
Eisenstein series	32	32	0

Trace form

128 * q - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^9 - 64 * q^12 + 16 * q^14 - 16 * q^15 - 16 * q^20 + 8 * q^22 - 32 * q^23 + 16 * q^26 + 32 * q^27 - 80 * q^31 - 16 * q^34 + 16 * q^36 + 16 * q^37 + 80 * q^38 - 112 * q^42 - 72 * q^44 - 16 * q^45 - 16 * q^47 + 32 * q^48 + 48 * q^49 - 16 * q^53 - 8 * q^55 - 16 * q^56 - 128 * q^58 + 48 * q^59 + 112 * q^60 + 48 * q^64 + 72 * q^66 - 192 * q^69 + 128 * q^70 - 16 * q^71 + 48 * q^75 + 8 * q^77 - 16 * q^78 + 112 * q^80 - 16 * q^82 + 32 * q^86 - 168 * q^88 - 16 * q^89 + 144 * q^91 - 176 * q^92 + 48 * q^93 + 48 * q^97 - 112 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(187, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
187.2.m.a	$187$	$2$	187.m	187.m	$16$	$128$	$16$	$1.493$		None		✓	✓	✓	187.2.m.a	$4$	$0$	\(0\)	\(-16\)	\(-16\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$