Space of modular forms of level 176, weight 2, and Character 176.x

• Label: 176.2.x
• Level: $176$
• Weight: $2$
• Character orbit: 176.x
• Rep. character: $\chi_{176}(19,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $176$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	176.x (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 176 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(176, [\chi])\).

	Total	New	Old
Modular forms	208	208	0
Cusp forms	176	176	0
Eisenstein series	32	32	0

Trace form

176 * q - 10 * q^2 - 6 * q^3 - 10 * q^4 - 6 * q^5 - 10 * q^6 - 20 * q^7 - 10 * q^8 - 4 * q^11 - 32 * q^12 - 10 * q^13 - 12 * q^14 + 14 * q^16 - 20 * q^17 + 40 * q^18 - 10 * q^19 - 14 * q^20 - 66 * q^22 - 16 * q^23 - 10 * q^24 + 56 * q^26 - 18 * q^27 - 10 * q^28 - 10 * q^29 - 50 * q^30 - 16 * q^33 - 4 * q^34 - 10 * q^35 - 22 * q^36 - 30 * q^37 + 22 * q^38 - 20 * q^39 - 10 * q^40 - 10 * q^42 - 46 * q^44 - 48 * q^45 - 30 * q^46 + 14 * q^48 + 8 * q^49 - 10 * q^50 - 10 * q^51 - 50 * q^52 + 18 * q^53 + 16 * q^55 + 8 * q^56 + 14 * q^58 + 10 * q^59 - 82 * q^60 - 10 * q^61 - 10 * q^62 + 38 * q^64 + 58 * q^66 - 56 * q^67 - 140 * q^68 - 24 * q^69 + 68 * q^70 + 20 * q^71 + 190 * q^72 + 40 * q^74 + 10 * q^75 - 14 * q^77 - 4 * q^78 + 148 * q^80 + 42 * q^82 - 110 * q^83 + 40 * q^84 - 10 * q^85 - 2 * q^86 + 182 * q^88 + 60 * q^90 + 54 * q^91 + 90 * q^92 - 18 * q^93 + 180 * q^94 + 90 * q^96 - 12 * q^97 - 68 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(176, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
176.2.x.a	$176$	$2$	176.x	176.x	$20$	$176$	$22$	$1.405$		None		✓	✓	✓	176.2.x.a	$4$	$0$	\(-10\)	\(-6\)	\(-6\)	\(-20\)		$\mathrm{SU}(2)[C_{20}]$