Newform orbit 280.3.y.a

• Label: 280.3.y.a
• Level: $280$
• Weight: $3$
• Character orbit: 280.y
• Analytic conductor: $7.629$
• Analytic rank: $0$
• Dimension: $184$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	280.y (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.62944740209\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 184 q - 4 q^{2} - 16 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
27.1	−1.99970	−	0.0345108i	−0.848603	−	0.848603i	3.99762	+	0.138022i	−2.25753	−	4.46134i	1.66767	+	1.72624i	4.28210	−	5.53748i	−7.98928	−	0.413965i		−	7.55975i	4.36042	+	8.99926i
27.2	−1.99970	−	0.0345108i	0.848603	+	0.848603i	3.99762	+	0.138022i	2.25753	+	4.46134i	−1.66767	−	1.72624i	5.53748	−	4.28210i	−7.98928	−	0.413965i		−	7.55975i	−4.36042	−	8.99926i
27.3	−1.97716	−	0.301385i	−2.49694	−	2.49694i	3.81833	+	1.19178i	4.55351	−	2.06532i	4.18432	+	5.68940i	−6.22790	−	3.19583i	−7.19028	−	3.50712i			3.46946i	−9.62548	+	2.71112i
27.4	−1.97716	−	0.301385i	2.49694	+	2.49694i	3.81833	+	1.19178i	−4.55351	+	2.06532i	−4.18432	−	5.68940i	3.19583	+	6.22790i	−7.19028	−	3.50712i			3.46946i	9.62548	−	2.71112i
27.5	−1.96277	+	0.384105i	−4.14813	−	4.14813i	3.70493	−	1.50782i	−4.49916	+	2.18118i	9.73514	+	6.54851i	−0.955190	−	6.93452i	−6.69276	+	4.38258i			25.4140i	7.99301	−	6.00931i
27.6	−1.96277	+	0.384105i	4.14813	+	4.14813i	3.70493	−	1.50782i	4.49916	−	2.18118i	−9.73514	−	6.54851i	6.93452	+	0.955190i	−6.69276	+	4.38258i			25.4140i	−7.99301	+	6.00931i
27.7	−1.95710	+	0.412029i	−2.78921	−	2.78921i	3.66046	−	1.61276i	4.84995	+	1.21573i	6.60800	+	4.30953i	6.31550	+	3.01901i	−6.49938	+	4.66455i			6.55943i	−9.99274	−	0.380981i
27.8	−1.95710	+	0.412029i	2.78921	+	2.78921i	3.66046	−	1.61276i	−4.84995	−	1.21573i	−6.60800	−	4.30953i	−3.01901	−	6.31550i	−6.49938	+	4.66455i			6.55943i	9.99274	+	0.380981i
27.9	−1.95051	+	0.442159i	−1.58132	−	1.58132i	3.60899	−	1.72487i	−2.43650	−	4.36617i	3.78357	+	2.38518i	−0.591687	+	6.97495i	−6.27671	+	4.96013i		−	3.99888i	6.68296	+	7.43895i
27.10	−1.95051	+	0.442159i	1.58132	+	1.58132i	3.60899	−	1.72487i	2.43650	+	4.36617i	−3.78357	−	2.38518i	−6.97495	+	0.591687i	−6.27671	+	4.96013i		−	3.99888i	−6.68296	−	7.43895i
27.11	−1.85428	−	0.749423i	−1.04956	−	1.04956i	2.87673	+	2.77928i	−2.49758	+	4.33152i	1.15962	+	2.73275i	−6.21366	−	3.22342i	−3.25141	−	7.30947i		−	6.79685i	7.87737	−	6.16012i
27.12	−1.85428	−	0.749423i	1.04956	+	1.04956i	2.87673	+	2.77928i	2.49758	−	4.33152i	−1.15962	−	2.73275i	3.22342	+	6.21366i	−3.25141	−	7.30947i		−	6.79685i	−7.87737	+	6.16012i
27.13	−1.81778	+	0.834077i	−1.65882	−	1.65882i	2.60863	−	3.03233i	−2.69633	+	4.21068i	4.39896	+	1.63179i	−3.01504	+	6.31740i	−2.21271	+	7.68791i		−	3.49660i	1.38929	−	9.90302i
27.14	−1.81778	+	0.834077i	1.65882	+	1.65882i	2.60863	−	3.03233i	2.69633	−	4.21068i	−4.39896	−	1.63179i	−6.31740	+	3.01504i	−2.21271	+	7.68791i		−	3.49660i	−1.38929	+	9.90302i
27.15	−1.80285	−	0.865861i	−2.52509	−	2.52509i	2.50057	+	3.12204i	0.456980	+	4.97907i	2.36600	+	6.73875i	4.25470	+	5.55855i	−1.80491	−	7.79373i			3.75218i	3.48731	−	9.37223i
27.16	−1.80285	−	0.865861i	2.52509	+	2.52509i	2.50057	+	3.12204i	−0.456980	−	4.97907i	−2.36600	−	6.73875i	−5.55855	−	4.25470i	−1.80491	−	7.79373i			3.75218i	−3.48731	+	9.37223i
27.17	−1.69251	−	1.06556i	−3.75369	−	3.75369i	1.72917	+	3.60693i	−3.22970	−	3.81694i	2.35338	+	10.3529i	−2.60987	+	6.49527i	0.916752	−	7.94730i			19.1804i	1.39912	+	9.90164i
27.18	−1.69251	−	1.06556i	3.75369	+	3.75369i	1.72917	+	3.60693i	3.22970	+	3.81694i	−2.35338	−	10.3529i	−6.49527	+	2.60987i	0.916752	−	7.94730i			19.1804i	−1.39912	−	9.90164i
27.19	−1.58918	+	1.21429i	−0.325945	−	0.325945i	1.05101	−	3.85945i	4.48039	−	2.21948i	0.913779	+	0.122195i	0.342794	−	6.99160i	3.01625	+	7.40960i		−	8.78752i	−4.42507	+	8.96765i
27.20	−1.58918	+	1.21429i	0.325945	+	0.325945i	1.05101	−	3.85945i	−4.48039	+	2.21948i	−0.913779	−	0.122195i	6.99160	−	0.342794i	3.01625	+	7.40960i		−	8.78752i	4.42507	−	8.96765i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
7.b	odd	2	1	inner
8.d	odd	2	1	inner
35.f	even	4	1	inner
40.k	even	4	1	inner
56.e	even	2	1	inner
280.y	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	280.3.y.a	✓	184
5.c	odd	4	1	inner	280.3.y.a	✓	184
7.b	odd	2	1	inner	280.3.y.a	✓	184
8.d	odd	2	1	inner	280.3.y.a	✓	184
35.f	even	4	1	inner	280.3.y.a	✓	184
40.k	even	4	1	inner	280.3.y.a	✓	184
56.e	even	2	1	inner	280.3.y.a	✓	184
280.y	odd	4	1	inner	280.3.y.a	✓	184

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
280.3.y.a	✓	184	1.a	even	1	1	trivial
280.3.y.a	✓	184	5.c	odd	4	1	inner
280.3.y.a	✓	184	7.b	odd	2	1	inner
280.3.y.a	✓	184	8.d	odd	2	1	inner
280.3.y.a	✓	184	35.f	even	4	1	inner
280.3.y.a	✓	184	40.k	even	4	1	inner
280.3.y.a	✓	184	56.e	even	2	1	inner
280.3.y.a	✓	184	280.y	odd	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(280, [\chi])\).