Newform orbit 152.3.r.a

• Label: 152.3.r.a
• Level: $152$
• Weight: $3$
• Character orbit: 152.r
• Analytic conductor: $4.142$
• Analytic rank: $0$
• Dimension: $60$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	152.r (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.14170001828\)
Analytic rank:	\(0\)
Dimension:	\(60\)
Relative dimension:	\(10\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 60 q + 6 q^{3} + 18 q^{9}+O(q^{10}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
33.1		0		−5.06444	−	0.892998i		0		−5.64832	−	4.73951i		0		4.67145	+	8.09119i		0		16.3939	+	5.96689i		0
33.2		0		−3.98504	−	0.702671i		0		2.78829	+	2.33966i		0		−0.472142	−	0.817775i		0		6.92959	+	2.52216i		0
33.3		0		−3.78874	−	0.668057i		0		4.65845	+	3.90890i		0		−4.65601	−	8.06445i		0		5.45102	+	1.98401i		0
33.4		0		−1.86549	−	0.328936i		0		−2.42977	−	2.03882i		0		2.67900	+	4.64016i		0		−5.08538	−	1.85093i		0
33.5		0		−0.220911	−	0.0389526i		0		−2.46245	−	2.06624i		0		−2.40895	−	4.17242i		0		−8.40995	−	3.06097i		0
33.6		0		1.30624	+	0.230325i		0		3.62531	+	3.04199i		0		3.54542	+	6.14085i		0		−6.80402	−	2.47646i		0
33.7		0		1.86146	+	0.328226i		0		−4.53951	−	3.80910i		0		−6.78466	−	11.7514i		0		−5.09993	−	1.85622i		0
33.8		0		3.25724	+	0.574339i		0		6.70213	+	5.62375i		0		−1.51839	−	2.62993i		0		1.82249	+	0.663334i		0
33.9		0		4.02296	+	0.709356i		0		−2.52114	−	2.11548i		0		5.99493	+	10.3835i		0		7.22375	+	2.62923i		0
33.10		0		5.82403	+	1.02693i		0		−0.172982	−	0.145149i		0		−2.43984	−	4.22593i		0		24.4075	+	8.88359i		0
41.1		0		−1.62171	−	4.45560i		0		−0.0546185	+	0.309757i		0		−3.67492	−	6.36515i		0		−10.3280	+	8.66625i		0
41.2		0		−1.60949	−	4.42204i		0		−1.72531	+	9.78470i		0		4.15775	+	7.20143i		0		−10.0696	+	8.44939i		0
41.3		0		−1.56299	−	4.29429i		0		1.50857	−	8.55551i		0		1.36572	+	2.36550i		0		−9.10355	+	7.63878i		0
41.4		0		−0.572077	−	1.57177i		0		0.151198	−	0.857485i		0		5.57607	+	9.65804i		0		4.75122	−	3.98675i		0
41.5		0		−0.255054	−	0.700754i		0		0.0111460	−	0.0632121i		0		−3.20124	−	5.54471i		0		6.46840	−	5.42763i		0
41.6		0		0.0188166	+	0.0516983i		0		−0.792124	+	4.49236i		0		1.45437	+	2.51904i		0		6.89208	−	5.78314i		0
41.7		0		0.680303	+	1.86912i		0		1.25622	−	7.12439i		0		−4.22930	−	7.32537i		0		3.86362	−	3.24196i		0
41.8		0		1.04427	+	2.86911i		0		1.09421	−	6.20558i		0		6.20011	+	10.7389i		0		−0.246871	+	0.207149i		0
41.9		0		1.20252	+	3.30390i		0		−0.888618	+	5.03960i		0		−0.753366	−	1.30487i		0		−2.57529	+	2.16092i		0
41.10		0		1.79603	+	4.93454i		0		−0.560676	+	3.17975i		0		0.622349	+	1.07794i		0		−14.2296	+	11.9400i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
19.f	odd	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	152.3.r.a	✓	60
4.b	odd	2	1		304.3.z.d		60
19.f	odd	18	1	inner	152.3.r.a	✓	60
76.k	even	18	1		304.3.z.d		60

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
152.3.r.a	✓	60	1.a	even	1	1	trivial
152.3.r.a	✓	60	19.f	odd	18	1	inner
304.3.z.d		60	4.b	odd	2	1
304.3.z.d		60	76.k	even	18	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(152, [\chi])\).