Newform orbit 64.7.j.a

• Label: 64.7.j.a
• Level: $64$
• Weight: $7$
• Character orbit: 64.j
• Analytic conductor: $14.723$
• Analytic rank: $0$
• Dimension: $376$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	64.j (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.7234613517\)
Analytic rank:	\(0\)
Dimension:	\(376\)
Relative dimension:	\(47\) over \(\Q(\zeta_{16})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 376 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 8 q^{5} - 8 q^{6} - 8 q^{7} - 8 q^{8} - 8 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
3.1	−7.99369	−	0.317693i	33.6917	+	6.70170i	63.7981	+	5.07907i	20.4370	+	13.6556i	−267.192	−	64.2749i	−212.330	−	512.609i	−508.369	−	60.8687i	416.711	+	172.607i	−159.029	−	115.651i
3.2	−7.99263	−	0.343362i	−45.2360	−	8.99800i	63.7642	+	5.48874i	−127.195	−	84.9891i	358.465	+	87.4500i	218.075	+	526.480i	−507.759	−	65.7636i	1291.82	+	535.091i	987.442	+	722.961i
3.3	−7.87514	−	1.40791i	14.7818	+	2.94029i	60.0356	+	22.1749i	−54.0661	−	36.1258i	−112.269	−	43.9666i	46.9711	+	113.398i	−441.568	−	259.155i	−463.651	−	192.051i	374.916	+	360.616i
3.4	−7.86826	+	1.44584i	−21.9073	−	4.35764i	59.8191	−	22.7524i	90.4060	+	60.4074i	178.673	+	2.61266i	−110.859	−	267.638i	−437.776	+	265.511i	−212.566	−	88.0477i	−798.678	−	344.589i
3.5	−7.56019	+	2.61600i	−9.26077	−	1.84208i	50.3131	−	39.5550i	26.0423	+	17.4009i	74.8321	−	10.2997i	93.4906	+	225.706i	−276.901	+	430.662i	−591.140	−	244.858i	−242.406	−	63.4275i
3.6	−7.34685	−	3.16605i	−43.3556	−	8.62396i	43.9523	+	46.5209i	49.8200	+	33.2887i	291.223	+	200.625i	−207.317	−	500.508i	−175.624	−	480.937i	1131.83	+	468.817i	−260.627	−	402.299i
3.7	−7.25854	+	3.36357i	41.7158	+	8.29778i	41.3728	−	48.8292i	−162.624	−	108.662i	−330.706	+	80.0841i	76.7557	+	185.305i	−136.065	+	493.589i	997.843	+	413.320i	1545.91	+	241.730i
3.8	−7.05477	−	3.77230i	−9.66662	−	1.92281i	35.5395	+	53.2254i	182.033	+	121.631i	60.9423	+	50.0304i	128.953	+	311.320i	−49.9403	−	509.559i	−583.762	−	241.802i	−825.375	−	1544.76i
3.9	−7.02383	+	3.82959i	39.3944	+	7.83604i	34.6684	−	53.7968i	198.419	+	132.579i	−306.709	+	95.8256i	98.1370	+	236.924i	−37.4851	+	510.626i	817.009	+	338.416i	−1901.39	−	171.351i
3.10	−6.60926	+	4.50751i	−21.1954	−	4.21603i	23.3647	−	59.5826i	−191.457	−	127.927i	159.090	−	67.6737i	−173.019	−	417.705i	114.146	+	499.114i	−242.037	−	100.255i	1842.02	−	17.4885i
3.11	−6.42006	−	4.77313i	47.5778	+	9.46381i	18.4344	+	61.2876i	9.39225	+	6.27570i	−260.280	−	287.853i	197.500	+	476.806i	174.184	−	481.460i	1500.57	+	621.558i	−30.3441	−	85.1208i
3.12	−6.24248	−	5.00315i	−7.68850	−	1.52934i	13.9370	+	62.4641i	−143.354	−	95.7860i	40.3438	+	48.0135i	−59.8096	−	144.393i	225.516	−	459.659i	−616.734	−	255.460i	415.651	+	1315.16i
3.13	−5.36515	+	5.93424i	14.9049	+	2.96478i	−6.43042	−	63.6761i	28.4401	+	19.0030i	−97.5609	+	72.5430i	−96.3125	−	232.519i	412.370	+	303.472i	−460.141	−	190.597i	−265.354	+	66.8161i
3.14	−5.34007	−	5.95681i	31.9584	+	6.35692i	−6.96726	+	63.6196i	124.019	+	82.8666i	−132.793	−	224.316i	−219.707	−	530.420i	416.176	−	298.231i	307.419	+	127.337i	−168.648	−	1181.27i
3.15	−5.19160	+	6.08665i	−42.7259	−	8.49871i	−10.0947	−	63.1989i	67.4080	+	45.0406i	273.544	−	215.936i	36.4038	+	87.8865i	437.077	+	266.660i	1079.77	+	447.254i	−624.101	+	176.456i
3.16	−4.08327	+	6.87945i	4.62549	+	0.920066i	−30.6537	−	56.1814i	−34.5708	−	23.0995i	−25.2167	+	28.0639i	256.860	+	620.114i	511.665	+	18.5230i	−652.960	−	270.465i	300.074	−	143.507i
3.17	−3.67029	−	7.10837i	−35.0021	−	6.96236i	−37.0579	+	52.1796i	12.4625	+	8.32721i	78.9770	+	274.362i	61.7240	+	149.015i	506.925	+	71.9073i	503.167	+	208.419i	13.4517	−	119.152i
3.18	−3.52255	−	7.18273i	19.6796	+	3.91451i	−39.1833	+	50.6031i	−24.8646	−	16.6140i	−41.2054	−	155.142i	83.2588	+	201.005i	501.493	+	103.191i	−301.546	−	124.905i	−31.7470	+	237.119i
3.19	−2.68729	+	7.53515i	38.7765	+	7.71312i	−49.5570	−	40.4982i	−63.0973	−	42.1603i	−162.323	+	271.459i	−128.651	−	310.591i	438.334	−	264.589i	770.616	+	319.200i	487.245	−	362.151i
3.20	−1.78702	+	7.79786i	−8.77753	−	1.74596i	−57.6131	−	27.8699i	180.457	+	120.578i	29.3004	−	65.3259i	−129.665	−	313.040i	320.281	−	399.455i	−599.511	−	248.326i	−1262.73	+	1191.70i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
64.j	odd	16	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	64.7.j.a	✓	376
64.j	odd	16	1	inner	64.7.j.a	✓	376

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
64.7.j.a	✓	376	1.a	even	1	1	trivial
64.7.j.a	✓	376	64.j	odd	16	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{7}^{\mathrm{new}}(64, [\chi])\).