Space of modular forms of level 152, weight 4, and Character 152.t

• Label: 152.4.t
• Level: $152$
• Weight: $4$
• Character orbit: 152.t
• Rep. character: $\chi_{152}(5,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $348$
• Newform subspaces: $1$
• Sturm bound: $80$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	152.t (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(80\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(152, [\chi])\).

	Total	New	Old
Modular forms	372	372	0
Cusp forms	348	348	0
Eisenstein series	24	24	0

Trace form

348 * q - 6 * q^2 + 12 * q^4 - 24 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9 + 75 * q^10 - 3 * q^12 - 81 * q^14 - 12 * q^15 + 192 * q^16 - 12 * q^17 - 12 * q^18 + 558 * q^20 - 30 * q^22 - 12 * q^23 - 108 * q^24 - 12 * q^25 - 411 * q^26 + 1140 * q^28 - 282 * q^30 - 1122 * q^31 + 39 * q^32 - 174 * q^33 + 1536 * q^34 - 2835 * q^36 + 966 * q^38 - 24 * q^39 - 1068 * q^40 + 48 * q^41 + 3015 * q^42 - 1203 * q^44 - 528 * q^46 - 624 * q^47 + 4755 * q^48 - 6768 * q^49 - 1074 * q^50 - 1089 * q^52 + 615 * q^54 - 762 * q^55 + 2046 * q^56 - 12 * q^57 + 4092 * q^58 + 4050 * q^60 + 3120 * q^62 + 2046 * q^63 + 2355 * q^64 - 6 * q^65 + 1716 * q^66 - 1176 * q^68 - 2973 * q^70 - 12 * q^71 - 7122 * q^72 + 636 * q^73 - 9363 * q^74 - 2454 * q^76 - 6897 * q^78 - 12 * q^79 - 6885 * q^80 + 1206 * q^81 - 7311 * q^82 + 1947 * q^84 + 7452 * q^86 - 6 * q^87 - 1131 * q^88 - 12 * q^89 + 4014 * q^90 + 7656 * q^92 + 11898 * q^94 + 1848 * q^95 - 18966 * q^96 - 12 * q^97 + 8055 * q^98

Decomposition of \(S_{4}^{\mathrm{new}}(152, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
152.4.t.a	$152$	$4$	152.t	152.t	$18$	$348$	$58$	$8.968$		None		✓	✓	✓	152.4.t.a	$4$	$0$	\(-6\)	\(0\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{18}]$