Space of modular forms of level 272, weight 3, and Character 272.i

• Label: 272.3.i
• Level: $272$
• Weight: $3$
• Character orbit: 272.i
• Rep. character: $\chi_{272}(251,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $140$
• Newform subspaces: $1$
• Sturm bound: $108$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 272 = 2^{4} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	272.i (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 272 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(108\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(272, [\chi])\).

	Total	New	Old
Modular forms	148	148	0
Cusp forms	140	140	0
Eisenstein series	8	8	0

Trace form

140 * q - 4 * q^4 - 6 * q^6 - 4 * q^7 - 396 * q^9 - 14 * q^10 + 6 * q^12 - 4 * q^13 + 44 * q^14 + 72 * q^15 + 52 * q^16 - 4 * q^17 - 20 * q^18 + 70 * q^20 - 4 * q^21 - 6 * q^22 - 4 * q^23 + 14 * q^24 - 620 * q^25 - 20 * q^26 + 12 * q^28 - 4 * q^29 - 40 * q^30 + 128 * q^31 - 60 * q^32 - 8 * q^33 + 90 * q^34 - 4 * q^35 + 36 * q^36 - 4 * q^38 - 4 * q^39 + 122 * q^40 + 176 * q^42 - 58 * q^44 + 244 * q^46 - 202 * q^48 - 20 * q^50 - 268 * q^52 - 164 * q^54 - 8 * q^55 + 116 * q^56 + 36 * q^57 + 138 * q^58 - 128 * q^59 + 76 * q^60 - 152 * q^62 + 356 * q^63 + 20 * q^64 + 12 * q^65 + 468 * q^66 - 4 * q^67 + 194 * q^68 + 188 * q^69 - 20 * q^70 - 260 * q^71 - 260 * q^72 - 48 * q^73 + 26 * q^74 + 304 * q^76 + 196 * q^77 - 692 * q^78 - 538 * q^80 + 964 * q^81 + 68 * q^82 - 4 * q^84 - 112 * q^85 + 24 * q^86 + 406 * q^88 + 126 * q^90 + 96 * q^92 + 36 * q^93 + 264 * q^94 + 100 * q^95 + 218 * q^96 - 4 * q^97 - 192 * q^98

Decomposition of \(S_{3}^{\mathrm{new}}(272, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
272.3.i.a	$272$	$3$	272.i	272.i	$4$	$140$	$70$	$7.411$		None		✓	✓	✓	272.3.i.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{4}]$