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

• Label: 152.4.o
• Level: $152$
• Weight: $4$
• Character orbit: 152.o
• Rep. character: $\chi_{152}(27,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $116$
• Newform subspaces: $2$
• Sturm bound: $80$
• Trace bound: $1$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	124	124	0
Cusp forms	116	116	0
Eisenstein series	8	8	0

Trace form

116 * q - 3 * q^2 - 6 * q^3 - 7 * q^4 - 23 * q^6 + 484 * q^9 + 96 * q^10 - 8 * q^11 + 120 * q^14 - 67 * q^16 - 2 * q^17 - 28 * q^19 + 576 * q^20 - 27 * q^22 - 11 * q^24 + 1248 * q^25 + 24 * q^26 + 94 * q^28 + 160 * q^30 + 357 * q^32 - 168 * q^33 + 414 * q^34 + 704 * q^35 + 616 * q^36 - 796 * q^38 + 888 * q^40 - 66 * q^41 + 458 * q^42 - 2 * q^43 + 857 * q^44 - 1359 * q^48 - 3796 * q^49 - 2238 * q^51 - 216 * q^52 + 1163 * q^54 + 282 * q^57 - 2944 * q^58 - 6 * q^59 - 1758 * q^60 + 542 * q^62 + 998 * q^64 - 2909 * q^66 - 6 * q^67 - 2676 * q^68 + 162 * q^70 + 1680 * q^72 + 214 * q^73 - 3660 * q^74 - 3321 * q^76 + 492 * q^78 - 1692 * q^80 - 3810 * q^81 - 1661 * q^82 - 2688 * q^83 - 1596 * q^86 - 6 * q^89 + 6720 * q^90 + 2052 * q^91 + 3106 * q^92 - 4126 * q^96 - 6 * q^97 + 1167 * q^98 + 1088 * q^99

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.o.a	$152$	$4$	152.o	152.o	$6$	$4$	$2$	$8.968$	$\Q(\sqrt{-2}, \sqrt{-3})$	$\Q(\sqrt{-2})$		✓			152.4.o.a	$4$	$0$	$0$	$-30$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{6}]$	$q+2\beta _{1}q^{2}+(-5+\beta _{1}-5\beta _{2})q^{3}+8\beta _{2}q^{4}+\cdots$
152.4.o.b	$152$	$4$	152.o	152.o	$6$	$112$	$56$	$8.968$		None		✓	✓		152.4.o.b	$4$	$0$	$-3$	$24$	$0$	$0$		$\mathrm{SU}(2)[C_{6}]$