Newform orbit 91.3.v.a

• Label: 91.3.v.a
• Level: $91$
• Weight: $3$
• Character orbit: 91.v
• Analytic conductor: $2.480$
• Analytic rank: $0$
• Dimension: $34$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	91.v (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.47957040568\)
Analytic rank:	\(0\)
Dimension:	\(34\)
Relative dimension:	\(17\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 34 q - 2 q^{2} + 62 q^{4} - 6 q^{5} - 24 q^{6} - 7 q^{7} - 16 q^{8} + 41 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
68.1	−3.68962			4.29521	+	2.47984i	9.61327			4.79181	+	2.76656i	−15.8477	−	9.14965i	−0.478190	−	6.98365i	−20.7108			7.79920	+	13.5086i	−17.6800	−	10.2075i
68.2	−3.47573			−0.729606	−	0.421238i	8.08067			−4.36801	−	2.52187i	2.53591	+	1.46411i	6.97149	+	0.631136i	−14.1833			−4.14512	−	7.17955i	15.1820	+	8.76534i
68.3	−3.20451			−1.49323	−	0.862117i	6.26891			2.69228	+	1.55439i	4.78508	+	2.76267i	−4.47700	+	5.38112i	−7.27076			−3.01351	−	5.21955i	−8.62746	−	4.98106i
68.4	−2.43740			−4.61760	−	2.66597i	1.94093			−3.34180	−	1.92939i	11.2549	+	6.49805i	−5.25110	−	4.62882i	5.01878			9.71482	+	16.8266i	8.14531	+	4.70270i
68.5	−1.98336			3.14196	+	1.81401i	−0.0662922			−8.23032	−	4.75178i	−6.23163	−	3.59783i	−4.62189	−	5.25720i	8.06491			2.08127	+	3.60486i	16.3237	+	9.42447i
68.6	−1.89761			2.67592	+	1.54494i	−0.399060			2.32671	+	1.34333i	−5.07786	−	2.93170i	−2.20092	+	6.64499i	8.34772			0.273690	+	0.474046i	−4.41520	−	2.54912i
68.7	−1.49942			−0.291045	−	0.168035i	−1.75174			1.72370	+	0.995181i	0.436399	+	0.251955i	5.62576	−	4.16543i	8.62427			−4.44353	−	7.69642i	−2.58455	−	1.49219i
68.8	−0.340003			−4.20872	−	2.42991i	−3.88440			5.75190	+	3.32086i	1.43098	+	0.826176i	2.56677	+	6.51243i	2.68072			7.30890	+	12.6594i	−1.95566	−	1.12910i
68.9	0.324673			4.27026	+	2.46543i	−3.89459			1.00609	+	0.580867i	1.38644	+	0.800459i	6.99926	+	0.102052i	−2.56316			7.65672	+	13.2618i	0.326651	+	0.188592i
68.10	0.431423			−0.498932	−	0.288058i	−3.81387			−6.18503	−	3.57093i	−0.215250	−	0.124275i	−1.26568	+	6.88462i	−3.37108			−4.33404	−	7.50679i	−2.66836	−	1.54058i
68.11	0.571667			−1.76273	−	1.01771i	−3.67320			−0.321261	−	0.185480i	−1.00770	−	0.581794i	−4.66237	−	5.22133i	−4.38651			−2.42851	−	4.20631i	−0.183654	−	0.106033i
68.12	1.58142			2.37172	+	1.36931i	−1.49910			7.02554	+	4.05620i	3.75069	+	2.16546i	−6.99770	−	0.179420i	−8.69641			−0.749964	−	1.29898i	11.1104	+	6.41457i
68.13	2.36721			−4.30191	−	2.48371i	1.60366			−5.80236	−	3.34999i	−10.1835	−	5.87945i	5.71735	−	4.03879i	−5.67263			7.83763	+	13.5752i	−13.7354	−	7.93012i
68.14	2.63624			−1.40558	−	0.811512i	2.94976			6.02670	+	3.47952i	−3.70544	−	2.13934i	6.42287	−	2.78330i	−2.76869			−3.18290	−	5.51294i	15.8878	+	9.17283i
68.15	2.78724			3.56192	+	2.05648i	3.76871			−4.47868	−	2.58577i	9.92794	+	5.73190i	−3.23811	−	6.20602i	−0.644649			3.95820	+	6.85581i	−12.4832	−	7.20716i
68.16	2.94111			1.39922	+	0.807840i	4.65014			−2.26684	−	1.30876i	4.11526	+	2.37595i	2.35876	+	6.59062i	1.91212			−3.19479	−	5.53353i	−6.66702	−	3.84921i
68.17	3.88667			−2.40684	−	1.38959i	11.1062			0.649554	+	0.375020i	−9.35460	−	5.40088i	−6.96931	+	0.654813i	27.6195			−0.638075	−	1.10518i	2.52460	+	1.45758i
87.1	−3.68962			4.29521	−	2.47984i	9.61327			4.79181	−	2.76656i	−15.8477	+	9.14965i	−0.478190	+	6.98365i	−20.7108			7.79920	−	13.5086i	−17.6800	+	10.2075i
87.2	−3.47573			−0.729606	+	0.421238i	8.08067			−4.36801	+	2.52187i	2.53591	−	1.46411i	6.97149	−	0.631136i	−14.1833			−4.14512	+	7.17955i	15.1820	−	8.76534i
87.3	−3.20451			−1.49323	+	0.862117i	6.26891			2.69228	−	1.55439i	4.78508	−	2.76267i	−4.47700	−	5.38112i	−7.27076			−3.01351	+	5.21955i	−8.62746	+	4.98106i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
91.v	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	91.3.v.a	yes	34
7.d	odd	6	1		91.3.m.a	✓	34
13.c	even	3	1		91.3.m.a	✓	34
91.v	odd	6	1	inner	91.3.v.a	yes	34

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
91.3.m.a	✓	34	7.d	odd	6	1
91.3.m.a	✓	34	13.c	even	3	1
91.3.v.a	yes	34	1.a	even	1	1	trivial
91.3.v.a	yes	34	91.v	odd	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(91, [\chi])\).