Newform orbit 960.3.be.a

• Label: 960.3.be.a
• Level: $960$
• Weight: $3$
• Character orbit: 960.be
• Analytic conductor: $26.158$
• Analytic rank: $0$
• Dimension: $96$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	960.be (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(26.1581053786\)
Analytic rank:	\(0\)
Dimension:	\(96\)
Relative dimension:	\(48\) over \(\Q(i)\)
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96 q + 288 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
337.1		0		−1.73205				0		4.62199	−	1.90716i		0		7.59279	−	7.59279i		0		3.00000				0
337.2		0		−1.73205				0		−0.202899	−	4.99588i		0		−7.08950	+	7.08950i		0		3.00000				0
337.3		0		−1.73205				0		−4.52664	+	2.12357i		0		−6.85443	+	6.85443i		0		3.00000				0
337.4		0		−1.73205				0		0.962977	+	4.90639i		0		6.59004	−	6.59004i		0		3.00000				0
337.5		0		−1.73205				0		1.44633	−	4.78625i		0		5.94516	−	5.94516i		0		3.00000				0
337.6		0		−1.73205				0		−4.87785	+	1.09845i		0		−4.66967	+	4.66967i		0		3.00000				0
337.7		0		−1.73205				0		−3.89880	−	3.13040i		0		−1.95568	+	1.95568i		0		3.00000				0
337.8		0		−1.73205				0		2.37096	−	4.40211i		0		−1.31097	+	1.31097i		0		3.00000				0
337.9		0		−1.73205				0		4.94986	+	0.706286i		0		−0.536990	+	0.536990i		0		3.00000				0
337.10		0		−1.73205				0		−2.91073	+	4.06542i		0		0.232675	−	0.232675i		0		3.00000				0
337.11		0		−1.73205				0		1.00692	+	4.89756i		0		0.348793	−	0.348793i		0		3.00000				0
337.12		0		−1.73205				0		4.19381	+	2.72249i		0		0.493893	−	0.493893i		0		3.00000				0
337.13		0		−1.73205				0		−0.425176	+	4.98189i		0		−0.992771	+	0.992771i		0		3.00000				0
337.14		0		−1.73205				0		−4.84784	+	1.22411i		0		−1.49053	+	1.49053i		0		3.00000				0
337.15		0		−1.73205				0		4.37932	−	2.41279i		0		−2.06325	+	2.06325i		0		3.00000				0
337.16		0		−1.73205				0		3.81012	−	3.23774i		0		−2.47993	+	2.47993i		0		3.00000				0
337.17		0		−1.73205				0		−2.57336	−	4.28694i		0		4.39445	−	4.39445i		0		3.00000				0
337.18		0		−1.73205				0		−3.96058	−	3.05186i		0		4.62313	−	4.62313i		0		3.00000				0
337.19		0		−1.73205				0		2.61912	+	4.25913i		0		−6.38794	+	6.38794i		0		3.00000				0
337.20		0		−1.73205				0		−4.67987	−	1.76034i		0		7.28155	−	7.28155i		0		3.00000				0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
80.t	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	960.3.be.a		96
4.b	odd	2	1		240.3.be.a	yes	96
5.c	odd	4	1		960.3.ba.a		96
16.e	even	4	1		960.3.ba.a		96
16.f	odd	4	1		240.3.ba.a	✓	96
20.e	even	4	1		240.3.ba.a	✓	96
80.j	even	4	1		240.3.be.a	yes	96
80.t	odd	4	1	inner	960.3.be.a		96

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
240.3.ba.a	✓	96	16.f	odd	4	1
240.3.ba.a	✓	96	20.e	even	4	1
240.3.be.a	yes	96	4.b	odd	2	1
240.3.be.a	yes	96	80.j	even	4	1
960.3.ba.a		96	5.c	odd	4	1
960.3.ba.a		96	16.e	even	4	1
960.3.be.a		96	1.a	even	1	1	trivial
960.3.be.a		96	80.t	odd	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(960, [\chi])\).