Space of modular forms of level 155, weight 2, and Character 155.x

• Label: 155.2.x
• Level: $155$
• Weight: $2$
• Character orbit: 155.x
• Rep. character: $\chi_{155}(3,\cdot)$
• Character field: $\Q(\zeta_{60})$
• Dimension: $224$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 155 = 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	155.x (of order \(60\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 155 \)
Character field:			\(\Q(\zeta_{60})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(155, [\chi])\).

	Total	New	Old
Modular forms	288	288	0
Cusp forms	224	224	0
Eisenstein series	64	64	0

Trace form

224 * q - 12 * q^2 - 14 * q^3 - 8 * q^5 - 36 * q^6 + 6 * q^7 - 40 * q^8 - 10 * q^10 - 28 * q^11 - 40 * q^12 - 14 * q^13 - 20 * q^15 + 24 * q^16 - 14 * q^17 - 40 * q^18 - 44 * q^20 - 44 * q^21 + 30 * q^22 - 30 * q^23 - 22 * q^25 - 48 * q^26 + 100 * q^27 - 48 * q^28 - 44 * q^31 + 28 * q^32 + 20 * q^33 - 72 * q^35 + 16 * q^36 + 30 * q^37 + 38 * q^38 - 4 * q^40 - 20 * q^41 - 130 * q^42 + 22 * q^43 - 34 * q^45 - 28 * q^47 - 156 * q^48 + 158 * q^50 - 36 * q^51 - 10 * q^52 + 26 * q^53 + 98 * q^55 - 48 * q^56 - 20 * q^58 + 260 * q^60 + 30 * q^62 + 152 * q^63 + 32 * q^65 - 152 * q^66 + 38 * q^67 - 126 * q^68 + 166 * q^70 - 128 * q^71 - 156 * q^72 - 30 * q^73 + 26 * q^75 + 128 * q^76 + 30 * q^78 + 154 * q^80 - 64 * q^81 + 8 * q^82 - 82 * q^83 + 60 * q^85 - 28 * q^86 - 24 * q^87 + 252 * q^88 + 38 * q^90 + 194 * q^93 - 74 * q^95 + 60 * q^96 - 38 * q^97 + 174 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(155, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
155.2.x.a	$155$	$2$	155.x	155.x	$60$	$224$	$14$	$1.238$		None		✓	✓	✓	155.2.x.a	$4$	$0$	\(-12\)	\(-14\)	\(-8\)	\(6\)		$\mathrm{SU}(2)[C_{60}]$