Newform orbit 65.4.l.a

• Label: 65.4.l.a
• Level: $65$
• Weight: $4$
• Character orbit: 65.l
• Analytic conductor: $3.835$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	65.l (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.83512415037\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(20\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 82 q^{4} - 6 q^{6} + 194 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
4.1	−2.78131	+	4.81737i	−5.79363	−	3.34495i	−11.4714	−	19.8690i	−5.89817	+	9.49798i	32.2277	−	18.6067i	4.32761	+	7.49564i	83.1206			8.87742	+	15.3761i	−29.3506	−	54.8305i
4.2	−2.44759	+	4.23936i	1.16314	+	0.671537i	−7.98143	−	13.8242i	4.99009	−	10.0049i	−5.69377	+	3.28730i	−14.4534	−	25.0340i	38.9797			−12.5981	−	21.8205i	30.2008	+	45.6428i
4.3	−2.32578	+	4.02837i	8.54577	+	4.93390i	−6.81851	−	11.8100i	−10.8920	+	2.52296i	−39.7512	+	22.9504i	2.60003	+	4.50339i	26.2209			35.1868	+	60.9454i	15.1689	−	49.7447i
4.4	−1.97935	+	3.42833i	2.98107	+	1.72112i	−3.83565	−	6.64354i	10.4428	+	3.99340i	−11.8011	+	6.81339i	14.8913	+	25.7925i	−1.30124			−7.57549	−	13.1211i	−34.3607	+	27.8972i
4.5	−1.59248	+	2.75826i	−7.71473	−	4.45410i	−1.07201	−	1.85677i	8.18270	−	7.61863i	24.5712	−	14.1862i	5.40541	+	9.36244i	−18.6511			26.1781	+	45.3418i	7.98337	+	34.7026i
4.6	−1.55778	+	2.69815i	−1.12086	−	0.647131i	−0.853359	−	1.47806i	−10.4184	−	4.05674i	3.49212	−	2.01617i	0.447020	+	0.774262i	−19.6071			−12.6624	−	21.9320i	27.1753	−	21.7909i
4.7	−1.23513	+	2.13931i	−4.10272	−	2.36870i	0.948888	+	1.64352i	2.46495	+	10.9052i	10.1348	−	5.85133i	−7.32744	−	12.6915i	−24.4502			−2.27848	−	3.94644i	−26.3743	−	8.19612i
4.8	−0.593564	+	1.02808i	7.13255	+	4.11798i	3.29536	+	5.70774i	11.0844	+	1.46126i	−8.46725	+	4.88857i	−15.6987	−	27.1910i	−17.3211			20.4155	+	35.3607i	−8.08162	+	10.5284i
4.9	−0.511032	+	0.885133i	3.59123	+	2.07340i	3.47769	+	6.02354i	−7.88807	+	7.92328i	−3.67046	+	2.11914i	−2.51873	−	4.36257i	−15.2854			−4.90206	−	8.49062i	−2.98210	−	11.0310i
4.10	−0.307922	+	0.533337i	4.12772	+	2.38314i	3.81037	+	6.59975i	0.679231	−	11.1597i	−2.54204	+	1.46765i	11.9145	+	20.6366i	−9.61995			−2.14128	−	3.70880i	5.74273	+	3.79858i
4.11	0.307922	−	0.533337i	−4.12772	−	2.38314i	3.81037	+	6.59975i	−0.679231	−	11.1597i	−2.54204	+	1.46765i	−11.9145	−	20.6366i	9.61995			−2.14128	−	3.70880i	−6.16103	−	3.07406i
4.12	0.511032	−	0.885133i	−3.59123	−	2.07340i	3.47769	+	6.02354i	7.88807	+	7.92328i	−3.67046	+	2.11914i	2.51873	+	4.36257i	15.2854			−4.90206	−	8.49062i	11.0442	−	2.93294i
4.13	0.593564	−	1.02808i	−7.13255	−	4.11798i	3.29536	+	5.70774i	−11.0844	+	1.46126i	−8.46725	+	4.88857i	15.6987	+	27.1910i	17.3211			20.4155	+	35.3607i	−5.07703	+	12.2631i
4.14	1.23513	−	2.13931i	4.10272	+	2.36870i	0.948888	+	1.64352i	−2.46495	+	10.9052i	10.1348	−	5.85133i	7.32744	+	12.6915i	24.4502			−2.27848	−	3.94644i	20.2852	+	18.7427i
4.15	1.55778	−	2.69815i	1.12086	+	0.647131i	−0.853359	−	1.47806i	10.4184	−	4.05674i	3.49212	−	2.01617i	−0.447020	−	0.774262i	19.6071			−12.6624	−	21.9320i	5.28386	−	34.4299i
4.16	1.59248	−	2.75826i	7.71473	+	4.45410i	−1.07201	−	1.85677i	−8.18270	−	7.61863i	24.5712	−	14.1862i	−5.40541	−	9.36244i	18.6511			26.1781	+	45.3418i	−34.0450	+	10.4375i
4.17	1.97935	−	3.42833i	−2.98107	−	1.72112i	−3.83565	−	6.64354i	−10.4428	+	3.99340i	−11.8011	+	6.81339i	−14.8913	−	25.7925i	1.30124			−7.57549	−	13.1211i	−6.97931	+	43.7059i
4.18	2.32578	−	4.02837i	−8.54577	−	4.93390i	−6.81851	−	11.8100i	10.8920	+	2.52296i	−39.7512	+	22.9504i	−2.60003	−	4.50339i	−26.2209			35.1868	+	60.9454i	35.4957	−	38.0090i
4.19	2.44759	−	4.23936i	−1.16314	−	0.671537i	−7.98143	−	13.8242i	−4.99009	−	10.0049i	−5.69377	+	3.28730i	14.4534	+	25.0340i	−38.9797			−12.5981	−	21.8205i	−54.6283	−	3.33327i
4.20	2.78131	−	4.81737i	5.79363	+	3.34495i	−11.4714	−	19.8690i	5.89817	+	9.49798i	32.2277	−	18.6067i	−4.32761	−	7.49564i	−83.1206			8.87742	+	15.3761i	62.1599	−	1.99688i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
13.e	even	6	1	inner
65.l	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	65.4.l.a	✓	40
5.b	even	2	1	inner	65.4.l.a	✓	40
13.e	even	6	1	inner	65.4.l.a	✓	40
65.l	even	6	1	inner	65.4.l.a	✓	40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
65.4.l.a	✓	40	1.a	even	1	1	trivial
65.4.l.a	✓	40	5.b	even	2	1	inner
65.4.l.a	✓	40	13.e	even	6	1	inner
65.4.l.a	✓	40	65.l	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(65, [\chi])\).