Space of modular forms of level 471, weight 2, and Character 471.w

• Label: 471.2.w
• Level: $471$
• Weight: $2$
• Character orbit: 471.w
• Rep. character: $\chi_{471}(5,\cdot)$
• Character field: $\Q(\zeta_{156})$
• Dimension: $2448$
• Newform subspaces: $2$
• Sturm bound: $105$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.w (of order \(156\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 471 \)
Character field:			\(\Q(\zeta_{156})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(105\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(471, [\chi])\).

	Total	New	Old
Modular forms	2640	2640	0
Cusp forms	2448	2448	0
Eisenstein series	192	192	0

Trace form

2448 * q - 52 * q^3 - 104 * q^4 - 52 * q^6 - 96 * q^7 - 48 * q^9 - 68 * q^10 - 10 * q^12 - 150 * q^13 - 60 * q^15 + 120 * q^16 - 60 * q^18 - 92 * q^19 - 46 * q^21 - 80 * q^22 - 84 * q^24 - 236 * q^25 - 52 * q^27 - 152 * q^28 - 38 * q^30 - 56 * q^31 - 70 * q^33 - 136 * q^34 - 130 * q^36 + 164 * q^37 - 94 * q^39 + 148 * q^40 - 94 * q^42 - 70 * q^43 - 20 * q^45 - 72 * q^46 + 178 * q^48 - 104 * q^49 + 2 * q^51 - 348 * q^52 + 186 * q^54 - 84 * q^55 - 46 * q^57 - 104 * q^58 - 182 * q^60 - 226 * q^61 - 50 * q^63 - 104 * q^64 - 20 * q^66 - 132 * q^67 - 164 * q^70 - 10 * q^72 - 22 * q^73 - 20 * q^75 - 176 * q^76 - 314 * q^78 - 126 * q^79 - 100 * q^81 - 104 * q^82 - 6 * q^84 + 56 * q^85 + 36 * q^87 - 112 * q^88 - 52 * q^90 - 498 * q^91 + 40 * q^93 - 336 * q^94 - 152 * q^96 - 196 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(471, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
471.2.w.a	$471$	$2$	471.w	471.w	$156$	$48$	$1$	$3.761$		\(\Q(\sqrt{-3}) \)		✓			471.2.w.a	$4$	$0$	\(0\)	\(-6\)	\(0\)	\(8\)		$\mathrm{U}(1)[D_{156}]$
471.2.w.b	$471$	$2$	471.w	471.w	$156$	$2400$	$50$	$3.761$		None		✓	✓		471.2.w.b	$4$	$0$	\(0\)	\(-46\)	\(0\)	\(-104\)		$\mathrm{SU}(2)[C_{156}]$