Newform orbit 560.2.be.a

• Label: 560.2.be.a
• Level: $560$
• Weight: $2$
• Character orbit: 560.be
• Analytic conductor: $4.472$
• Analytic rank: $0$
• Dimension: $184$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.be (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(4.47162251319\)
Analytic rank:	\(0\)
Dimension:	\(184\)
Relative dimension:	\(92\) over \(\Q(i)\)
Twist minimal:	yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 184 q - 8 q^{4}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
139.1	−1.41383	−	0.0328882i	−1.31817	−	1.31817i	1.99784	+	0.0929966i	1.05420	−	1.97197i	1.82031	+	1.90702i	2.24452	−	1.40075i	−2.82155	−	0.197187i			0.475122i	−1.55532	+	2.75336i
139.2	−1.41383	−	0.0328882i	1.31817	+	1.31817i	1.99784	+	0.0929966i	−1.05420	+	1.97197i	−1.82031	−	1.90702i	−2.24452	−	1.40075i	−2.82155	−	0.197187i			0.475122i	1.55532	−	2.75336i
139.3	−1.40363	+	0.172701i	−0.710544	−	0.710544i	1.94035	−	0.484816i	1.39309	+	1.74909i	1.12005	+	0.874629i	−2.62345	+	0.342784i	−2.63980	+	1.01560i		−	1.99025i	−2.25745	−	2.21448i
139.4	−1.40363	+	0.172701i	0.710544	+	0.710544i	1.94035	−	0.484816i	−1.39309	−	1.74909i	−1.12005	−	0.874629i	2.62345	+	0.342784i	−2.63980	+	1.01560i		−	1.99025i	2.25745	+	2.21448i
139.5	−1.40049	−	0.196510i	−1.64523	−	1.64523i	1.92277	+	0.550422i	−1.65460	+	1.50409i	1.98083	+	2.62744i	−0.240324	+	2.63481i	−2.58466	−	1.14871i			2.41357i	2.61283	−	1.78133i
139.6	−1.40049	−	0.196510i	1.64523	+	1.64523i	1.92277	+	0.550422i	1.65460	−	1.50409i	−1.98083	−	2.62744i	0.240324	+	2.63481i	−2.58466	−	1.14871i			2.41357i	−2.61283	+	1.78133i
139.7	−1.33517	−	0.466181i	−1.96435	−	1.96435i	1.56535	+	1.24486i	0.776425	+	2.09694i	1.70699	+	3.53848i	1.99873	−	1.73352i	−1.50968	−	2.39184i			4.71733i	−0.0591043	−	3.16173i
139.8	−1.33517	−	0.466181i	1.96435	+	1.96435i	1.56535	+	1.24486i	−0.776425	−	2.09694i	−1.70699	−	3.53848i	−1.99873	−	1.73352i	−1.50968	−	2.39184i			4.71733i	0.0591043	+	3.16173i
139.9	−1.30971	+	0.533547i	−1.34417	−	1.34417i	1.43065	−	1.39758i	−2.08996	+	0.795024i	2.47764	+	1.04329i	0.486119	−	2.60071i	−1.12806	+	2.59374i			0.613574i	2.31305	−	2.15634i
139.10	−1.30971	+	0.533547i	1.34417	+	1.34417i	1.43065	−	1.39758i	2.08996	−	0.795024i	−2.47764	−	1.04329i	−0.486119	−	2.60071i	−1.12806	+	2.59374i			0.613574i	−2.31305	+	2.15634i
139.11	−1.30750	−	0.538918i	−0.289321	−	0.289321i	1.41913	+	1.40928i	−2.02485	−	0.948664i	0.222368	+	0.534210i	−1.73658	+	1.99607i	−1.09604	−	2.60743i		−	2.83259i	2.13625	+	2.33161i
139.12	−1.30750	−	0.538918i	0.289321	+	0.289321i	1.41913	+	1.40928i	2.02485	+	0.948664i	−0.222368	−	0.534210i	1.73658	+	1.99607i	−1.09604	−	2.60743i		−	2.83259i	−2.13625	−	2.33161i
139.13	−1.27264	+	0.616746i	−0.0442516	−	0.0442516i	1.23925	−	1.56980i	−0.0460683	+	2.23559i	0.0836085	+	0.0290246i	2.16475	+	1.52114i	−0.608959	+	2.76210i		−	2.99608i	−1.32016	−	2.87353i
139.14	−1.27264	+	0.616746i	0.0442516	+	0.0442516i	1.23925	−	1.56980i	0.0460683	−	2.23559i	−0.0836085	−	0.0290246i	−2.16475	+	1.52114i	−0.608959	+	2.76210i		−	2.99608i	1.32016	+	2.87353i
139.15	−1.22124	−	0.713144i	−0.422516	−	0.422516i	0.982851	+	1.74184i	1.94457	−	1.10393i	0.214678	+	0.817308i	−1.83593	−	1.90509i	0.0418853	−	2.82812i		−	2.64296i	−3.16204	−	0.0385979i
139.16	−1.22124	−	0.713144i	0.422516	+	0.422516i	0.982851	+	1.74184i	−1.94457	+	1.10393i	−0.214678	−	0.817308i	1.83593	−	1.90509i	0.0418853	−	2.82812i		−	2.64296i	3.16204	+	0.0385979i
139.17	−1.16263	+	0.805161i	−2.03615	−	2.03615i	0.703430	−	1.87221i	−1.56280	−	1.59927i	4.00673	+	0.727866i	0.889133	+	2.49188i	0.689603	+	2.74307i			5.29182i	3.10463	+	0.601051i
139.18	−1.16263	+	0.805161i	2.03615	+	2.03615i	0.703430	−	1.87221i	1.56280	+	1.59927i	−4.00673	−	0.727866i	−0.889133	+	2.49188i	0.689603	+	2.74307i			5.29182i	−3.10463	−	0.601051i
139.19	−1.15591	+	0.814782i	−2.22344	−	2.22344i	0.672261	−	1.88363i	2.21099	+	0.333957i	4.38172	+	0.758481i	−1.99535	−	1.73741i	0.757674	+	2.72506i			6.88739i	−2.82781	+	1.41545i
139.20	−1.15591	+	0.814782i	2.22344	+	2.22344i	0.672261	−	1.88363i	−2.21099	−	0.333957i	−4.38172	−	0.758481i	1.99535	−	1.73741i	0.757674	+	2.72506i			6.88739i	2.82781	−	1.41545i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
7.b	odd	2	1	inner
16.f	odd	4	1	inner
35.c	odd	2	1	inner
80.k	odd	4	1	inner
112.j	even	4	1	inner
560.be	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	560.2.be.a	✓	184
5.b	even	2	1	inner	560.2.be.a	✓	184
7.b	odd	2	1	inner	560.2.be.a	✓	184
16.f	odd	4	1	inner	560.2.be.a	✓	184
35.c	odd	2	1	inner	560.2.be.a	✓	184
80.k	odd	4	1	inner	560.2.be.a	✓	184
112.j	even	4	1	inner	560.2.be.a	✓	184
560.be	even	4	1	inner	560.2.be.a	✓	184

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
560.2.be.a	✓	184	1.a	even	1	1	trivial
560.2.be.a	✓	184	5.b	even	2	1	inner
560.2.be.a	✓	184	7.b	odd	2	1	inner
560.2.be.a	✓	184	16.f	odd	4	1	inner
560.2.be.a	✓	184	35.c	odd	2	1	inner
560.2.be.a	✓	184	80.k	odd	4	1	inner
560.2.be.a	✓	184	112.j	even	4	1	inner
560.2.be.a	✓	184	560.be	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(560, [\chi])\).