Space of modular forms of level 152, weight 3, and Character 152.n

• Label: 152.3.n
• Level: $152$
• Weight: $3$
• Character orbit: 152.n
• Rep. character: $\chi_{152}(65,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	152.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(60\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(152, [\chi])\).

	Total	New	Old
Modular forms	88	20	68
Cusp forms	72	20	52
Eisenstein series	16	0	16

Trace form

20 * q - 6 * q^3 - 16 * q^7 + 24 * q^9 + 20 * q^11 - 12 * q^13 - 24 * q^15 + 28 * q^17 - 26 * q^19 + 36 * q^21 + 56 * q^23 - 34 * q^25 + 48 * q^29 - 18 * q^33 - 20 * q^35 - 56 * q^39 - 42 * q^41 + 100 * q^43 - 128 * q^45 - 48 * q^47 - 100 * q^49 + 36 * q^53 - 72 * q^55 + 332 * q^57 - 246 * q^59 - 80 * q^61 + 4 * q^63 - 258 * q^67 - 36 * q^71 - 94 * q^73 - 112 * q^77 + 216 * q^79 - 382 * q^81 + 76 * q^83 - 52 * q^85 + 496 * q^87 + 432 * q^89 + 432 * q^91 + 84 * q^93 - 388 * q^95 + 570 * q^97 + 248 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(152, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
152.3.n.a	$152$	$3$	152.n	19.d	$6$	$20$	$10$	$4.142$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		✓	✓	✓	152.3.n.a	$2$	$0$	\(0\)	\(-6\)	\(0\)	\(-16\)	$2^{14}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{3}+\beta _{19}q^{5}+(-1-\beta _{3})q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(152, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(152, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)