Newform orbit 91.5.x.a

• Label: 91.5.x.a
• Level: $91$
• Weight: $5$
• Character orbit: 91.x
• Analytic conductor: $9.407$
• Analytic rank: $0$
• Dimension: $140$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	91.x (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.40666664063\)
Analytic rank:	\(0\)
Dimension:	\(140\)
Relative dimension:	\(35\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 140 q - 2 q^{2} + 2 q^{3} - 2 q^{5} - 40 q^{6} - 118 q^{7} + 24 q^{8} - 1618 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
2.1	−5.42039	+	5.42039i	−2.43959	+	4.22549i		−	42.7613i	−7.61041	−	28.4024i	−9.68030	−	36.1274i	−29.8105	−	38.8887i	145.057	+	145.057i	28.5968	+	49.5311i	195.204	+	112.701i
2.2	−5.28732	+	5.28732i	6.02228	−	10.4309i		−	39.9116i	3.08494	+	11.5131i	23.3098	+	86.9932i	−35.2438	+	34.0423i	126.428	+	126.428i	−32.0357	−	55.4875i	−77.1847	−	44.5626i
2.3	−4.84387	+	4.84387i	−7.75925	+	13.4394i		−	30.9261i	11.5786	+	43.2120i	−27.5140	−	102.684i	−47.4151	−	12.3617i	72.3003	+	72.3003i	−79.9119	−	138.411i	−265.399	−	153.228i
2.4	−4.67577	+	4.67577i	−4.29238	+	7.43461i		−	27.7256i	−2.56372	−	9.56792i	−14.6924	−	54.8327i	48.9606	+	1.96356i	54.8261	+	54.8261i	3.65101	+	6.32374i	56.7247	+	32.7500i
2.5	−4.53118	+	4.53118i	−1.11725	+	1.93513i		−	25.0632i	5.74733	+	21.4493i	−3.70597	−	13.8309i	26.7168	+	41.0757i	41.0668	+	41.0668i	38.0035	+	65.8240i	−123.233	−	71.1485i
2.6	−4.41246	+	4.41246i	6.76831	−	11.7231i		−	22.9396i	−7.45075	−	27.8066i	21.8626	+	81.5925i	42.9993	−	23.4960i	30.6209	+	30.6209i	−51.1200	−	88.5425i	155.572	+	89.8193i
2.7	−3.90010	+	3.90010i	4.38803	−	7.60029i		−	14.4215i	8.56043	+	31.9479i	12.5281	+	46.7556i	3.46426	−	48.8774i	−6.15619	−	6.15619i	1.99043	+	3.44752i	−157.987	−	91.2136i
2.8	−3.72166	+	3.72166i	1.30796	−	2.26546i		−	11.7014i	−9.59597	−	35.8127i	3.56347	+	13.2990i	−41.9963	+	25.2450i	−15.9978	−	15.9978i	37.0785	+	64.2218i	168.995	+	97.5695i
2.9	−2.94084	+	2.94084i	−0.105321	+	0.182421i		−	1.29709i	1.71710	+	6.40832i	−0.226739	−	0.846202i	−33.6827	−	35.5876i	−43.2389	−	43.2389i	40.4778	+	70.1096i	−23.8956	−	13.7961i
2.10	−2.77985	+	2.77985i	−6.61842	+	11.4634i			0.544843i	−4.81540	−	17.9713i	−13.4684	−	50.2649i	−18.1534	+	45.5132i	−45.9922	−	45.9922i	−47.1069	−	81.5915i	63.3437	+	36.5715i
2.11	−2.67550	+	2.67550i	−7.09925	+	12.2963i			1.68340i	−3.59607	−	13.4207i	−13.9046	−	51.8927i	18.2188	−	45.4871i	−47.3119	−	47.3119i	−60.2988	−	104.441i	45.5284	+	26.2858i
2.12	−2.33093	+	2.33093i	4.88590	−	8.46263i			5.13354i	−3.54397	−	13.2263i	8.33710	+	31.1145i	36.8963	+	32.2438i	−49.2608	−	49.2608i	−7.24408	−	12.5471i	39.0903	+	22.5688i
2.13	−1.77214	+	1.77214i	7.52874	−	13.0402i			9.71904i	9.30516	+	34.7273i	9.76700	+	36.4509i	−14.6089	+	46.7716i	−45.5777	−	45.5777i	−72.8637	−	126.204i	−78.0317	−	45.0516i
2.14	−1.26742	+	1.26742i	−3.58178	+	6.20383i			12.7873i	7.27456	+	27.1490i	−3.32324	−	12.4025i	−36.8151	+	32.3365i	−36.4857	−	36.4857i	14.8417	+	25.7066i	−43.6293	−	25.1894i
2.15	−1.20816	+	1.20816i	−1.31946	+	2.28538i			13.0807i	8.44785	+	31.5278i	−1.16698	−	4.35524i	47.8544	−	10.5338i	−35.1342	−	35.1342i	37.0180	+	64.1171i	−48.2972	−	27.8844i
2.16	−0.980907	+	0.980907i	5.77547	−	10.0034i			14.0756i	−6.11845	−	22.8344i	4.14722	+	15.4776i	−46.7390	−	14.7127i	−29.5014	−	29.5014i	−26.2122	−	45.4008i	28.4000	+	16.3968i
2.17	−0.241331	+	0.241331i	−1.56686	+	2.71388i			15.8835i	−9.61481	−	35.8830i	−0.276811	−	1.03307i	34.4819	+	34.8138i	−7.69447	−	7.69447i	35.5899	+	61.6435i	10.9800	+	6.33931i
2.18	−0.0369256	+	0.0369256i	−0.260045	+	0.450411i			15.9973i	−5.97810	−	22.3106i	−0.00702939	−	0.0262341i	25.4005	−	41.9024i	−1.18152	−	1.18152i	40.3648	+	69.9138i	1.04458	+	0.603087i
2.19	0.223914	−	0.223914i	7.49742	−	12.9859i			15.8997i	−0.677485	−	2.52841i	−1.22895	−	4.58649i	12.1591	−	47.4674i	7.14278	+	7.14278i	−71.9225	−	124.573i	−0.717843	−	0.414447i
2.20	0.959270	−	0.959270i	−8.24263	+	14.2767i			14.1596i	4.67406	+	17.4438i	5.78826	+	21.6021i	34.2576	+	35.0346i	28.9312	+	28.9312i	−95.3819	−	165.206i	21.2170	+	12.2497i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
91.x	odd	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	91.5.x.a	✓	140
7.c	even	3	1		91.5.bd.a	yes	140
13.f	odd	12	1		91.5.bd.a	yes	140
91.x	odd	12	1	inner	91.5.x.a	✓	140

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
91.5.x.a	✓	140	1.a	even	1	1	trivial
91.5.x.a	✓	140	91.x	odd	12	1	inner
91.5.bd.a	yes	140	7.c	even	3	1
91.5.bd.a	yes	140	13.f	odd	12	1

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(91, [\chi])\).