Newform orbit 280.3.z.a

• Label: 280.3.z.a
• Level: $280$
• Weight: $3$
• Character orbit: 280.z
• Analytic conductor: $7.629$
• Analytic rank: $0$
• Dimension: $128$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	280.z (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.62944740209\)
Analytic rank:	\(0\)
Dimension:	\(128\)
Relative dimension:	\(64\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 128 q - 2 q^{2} + 6 q^{4} - 20 q^{8} - 192 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
11.1	−1.99241	+	0.174081i	2.16619	−	3.75195i	3.93939	−	0.693681i	1.93649	−	1.11803i	−3.66280	+	7.85252i	−5.66255	+	4.11528i	−7.72813	+	2.06787i	−4.88478	−	8.46068i	−3.66366	+	2.56469i
11.2	−1.98302	+	0.260023i	2.36323	−	4.09323i	3.86478	−	1.03126i	−1.93649	+	1.11803i	−3.62200	+	8.73147i	5.40672	−	4.44605i	−7.39579	+	3.04995i	−6.66969	−	11.5522i	3.54940	−	2.72062i
11.3	−1.96643	+	0.364909i	−2.18667	+	3.78742i	3.73368	−	1.43514i	−1.93649	+	1.11803i	2.91786	−	8.24562i	6.71890	−	1.96378i	−6.81833	+	4.18455i	−5.06302	−	8.76941i	3.39999	−	2.90518i
11.4	−1.94313	+	0.473551i	−0.0531403	+	0.0920417i	3.55150	−	1.84034i	−1.93649	+	1.11803i	0.0596720	−	0.204013i	−5.49200	−	4.34027i	−6.02952	+	5.25784i	4.49435	+	7.78445i	3.23341	−	3.08951i
11.5	−1.94216	−	0.477526i	0.138292	−	0.239528i	3.54394	+	1.85486i	1.93649	−	1.11803i	−0.382965	+	0.399163i	6.49683	−	2.60599i	−5.99713	−	5.29475i	4.46175	+	7.72798i	−4.29486	+	1.24667i
11.6	−1.94194	−	0.478386i	−1.25635	+	2.17607i	3.54229	+	1.85800i	1.93649	−	1.11803i	3.48077	−	3.62478i	−6.04823	+	3.52406i	−5.99009	−	5.30272i	1.34316	+	2.32642i	−4.29541	+	1.24477i
11.7	−1.92751	−	0.533592i	−2.69599	+	4.66960i	3.43056	+	2.05700i	−1.93649	+	1.11803i	7.68820	−	7.56212i	−6.70668	+	2.00509i	−5.51483	−	5.79540i	−10.0368	−	17.3842i	4.32917	−	1.12172i
11.8	−1.90188	+	0.618762i	−1.37248	+	2.37721i	3.23427	−	2.35362i	1.93649	−	1.11803i	1.13937	−	5.37041i	−3.02373	−	6.31325i	−4.69485	+	6.47753i	0.732571	+	1.26885i	−2.99117	+	3.32459i
11.9	−1.86395	−	0.725055i	1.75983	−	3.04812i	2.94859	+	2.70293i	−1.93649	+	1.11803i	−5.49029	+	4.40556i	1.99414	+	6.70995i	−3.53624	−	7.17600i	−1.69403	−	2.93415i	4.42015	−	0.679892i
11.10	−1.85626	+	0.744505i	−2.53196	+	4.38548i	2.89143	−	2.76399i	1.93649	−	1.11803i	1.43497	−	10.0257i	5.33290	+	4.53433i	−3.30944	+	7.28338i	−8.32165	−	14.4135i	−2.76226	+	3.51709i
11.11	−1.78185	+	0.908297i	1.30869	−	2.26672i	2.34999	−	3.23690i	1.93649	−	1.11803i	−0.273038	+	5.22763i	4.46493	+	5.39114i	−1.24727	+	7.90217i	1.07466	+	1.86137i	−2.43503	+	3.75108i
11.12	−1.76149	−	0.947183i	0.110018	−	0.190557i	2.20569	+	3.33690i	−1.93649	+	1.11803i	−0.374288	+	0.231457i	−1.90973	−	6.73446i	−0.724642	−	7.96711i	4.47579	+	7.75230i	4.47009	−	0.135194i
11.13	−1.67276	−	1.09630i	−1.47853	+	2.56089i	1.59624	+	3.66770i	−1.93649	+	1.11803i	5.28074	−	2.66284i	6.99634	−	0.226470i	1.35078	−	7.88514i	0.127889	+	0.221510i	4.46499	+	0.252779i
11.14	−1.64081	+	1.14356i	1.91036	−	3.30884i	1.38454	−	3.75274i	−1.93649	+	1.11803i	0.649316	+	7.61380i	−6.82895	+	1.53799i	2.01972	+	7.74085i	−2.79895	−	4.84792i	1.89888	−	4.04898i
11.15	−1.52151	−	1.29808i	−2.60128	+	4.50554i	0.629988	+	3.95008i	1.93649	−	1.11803i	9.80641	−	3.47857i	−0.235164	−	6.99605i	4.16897	−	6.82786i	−9.03328	−	15.6461i	−4.39769	−	0.812616i
11.16	−1.49582	+	1.32760i	−0.907232	+	1.57137i	0.474976	−	3.97170i	−1.93649	+	1.11803i	−0.729088	−	3.55493i	−0.105692	+	6.99920i	4.56233	+	6.57154i	2.85386	+	4.94303i	1.41235	−	4.24326i
11.17	−1.44597	−	1.38173i	2.76803	−	4.79437i	0.181641	+	3.99587i	1.93649	−	1.11803i	−10.6270	+	3.10783i	6.66406	+	2.14249i	5.25858	−	6.02888i	−10.8240	−	18.7477i	−4.34492	−	1.05907i
11.18	−1.28084	−	1.53605i	0.719622	−	1.24642i	−0.718912	+	3.93487i	1.93649	−	1.11803i	−2.83629	+	0.491087i	−6.75282	+	1.84374i	6.96497	−	3.93564i	3.46429	+	6.00032i	−4.19769	−	1.54253i
11.19	−1.21029	+	1.59223i	0.436622	−	0.756252i	−1.07041	−	3.85412i	1.93649	−	1.11803i	0.675691	+	1.61049i	−6.36853	−	2.90548i	7.43216	+	2.96024i	4.11872	+	7.13384i	−0.563540	+	4.43649i
11.20	−1.16048	+	1.62889i	−1.76372	+	3.05485i	−1.30658	−	3.78059i	−1.93649	+	1.11803i	−2.92926	−	6.41799i	2.91329	−	6.36496i	7.67443	+	2.25903i	−1.72139	−	2.98153i	0.426102	−	4.45179i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.c	even	3	1	inner
8.d	odd	2	1	inner
56.k	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	280.3.z.a	✓	128
7.c	even	3	1	inner	280.3.z.a	✓	128
8.d	odd	2	1	inner	280.3.z.a	✓	128
56.k	odd	6	1	inner	280.3.z.a	✓	128

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
280.3.z.a	✓	128	1.a	even	1	1	trivial
280.3.z.a	✓	128	7.c	even	3	1	inner
280.3.z.a	✓	128	8.d	odd	2	1	inner
280.3.z.a	✓	128	56.k	odd	6	1	inner

Hecke kernels

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