Newform orbit 91.10.e.a

• Label: 91.10.e.a
• Level: $91$
• Weight: $10$
• Character orbit: 91.e
• Analytic conductor: $46.868$
• Analytic rank: $0$
• Dimension: $70$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	91.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(46.8682610909\)
Analytic rank:	\(0\)
Dimension:	\(70\)
Relative dimension:	\(35\) over \(\Q(\zeta_{3})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 70 q + 65 q^{2} - 8533 q^{4} - 2118 q^{5} + 17358 q^{6} - 8764 q^{7} - 106980 q^{8} - 215597 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
53.1	−21.7445	−	37.6626i	−31.2108	+	54.0587i	−689.647	+	1194.50i	146.760	+	254.196i	2714.65			−5982.50	+	2136.18i	37717.8			7893.27	+	13671.5i	6382.45	−	11054.7i
53.2	−19.4314	−	33.6561i	−91.9975	+	159.344i	−499.156	+	864.564i	723.891	+	1253.82i	7150.55			13.7108	−	6352.43i	18899.4			−7085.57	−	12272.6i	28132.4	−	48726.7i
53.3	−18.4208	−	31.9058i	63.9657	−	110.792i	−422.654	+	732.058i	169.293	+	293.224i	−4713.21			1350.37	−	6207.26i	12279.6			1658.27	+	2872.20i	6237.03	−	10802.9i
53.4	−18.1742	−	31.4787i	−22.4027	+	38.8026i	−404.604	+	700.795i	−449.239	−	778.105i	1628.61			2896.03	+	5653.90i	10803.1			8837.74	+	15307.4i	−16329.1	+	28282.9i
53.5	−17.8760	−	30.9621i	96.3548	−	166.891i	−383.101	+	663.550i	−1261.17	−	2184.41i	−6889.74			−4557.75	−	4424.99i	9088.22			−8726.99	−	15115.6i	−45089.4	+	78097.1i
53.6	−16.2746	−	28.1884i	60.6201	−	104.997i	−273.726	+	474.107i	1179.89	+	2043.63i	−3946.27			−2105.73	+	5993.29i	1153.91			2491.91	+	4316.12i	38404.6	−	66518.7i
53.7	−15.4941	−	26.8366i	−87.7424	+	151.974i	−224.136	+	388.215i	−994.442	−	1722.42i	5437.97			5647.80	−	2907.91i	−1974.83			−5555.97	−	9623.22i	−30816.0	+	53374.9i
53.8	−11.6654	−	20.2051i	−114.632	+	198.549i	−16.1632	+	27.9955i	−540.667	−	936.463i	5348.93			−5257.21	+	3565.86i	−11191.2			−16439.7	−	28474.3i	−12614.2	+	21848.4i
53.9	−10.6060	−	18.3701i	42.6958	−	73.9513i	31.0274	−	53.7410i	422.676	+	732.096i	−1811.32			6099.93	−	1773.28i	−12176.8			6195.64	+	10731.2i	8965.77	−	15529.2i
53.10	−9.68351	−	16.7723i	−16.9452	+	29.3499i	68.4592	−	118.575i	−732.091	−	1268.02i	656.356			−5194.70	−	3656.32i	−12567.6			9267.22	+	16051.3i	−14178.4	+	24557.7i
53.11	−9.60109	−	16.6296i	−128.933	+	223.318i	71.6381	−	124.081i	679.560	+	1177.03i	4951.58			6297.72	−	832.067i	−12582.7			−23405.8	−	40540.0i	13049.0	−	22601.6i
53.12	−8.75534	−	15.1647i	126.100	−	218.411i	102.688	−	177.861i	−351.181	−	608.263i	−4416.19			−5379.03	+	3379.30i	−12561.7			−21960.9	−	38037.3i	−6149.41	+	10651.1i
53.13	−7.79810	−	13.5067i	70.3015	−	121.766i	134.379	−	232.752i	740.523	+	1282.62i	−2192.87			−6071.29	−	1868.97i	−12176.9			−43.0895	−	74.6332i	11549.3	−	20004.1i
53.14	−4.24872	−	7.35900i	43.1429	−	74.7257i	219.897	−	380.872i	−1055.39	−	1827.99i	−733.208			4469.67	+	4513.94i	−8087.81			6118.88	+	10598.2i	−8968.10	+	15533.2i
53.15	−4.19848	−	7.27198i	−49.8365	+	86.3193i	220.745	−	382.342i	1320.17	+	2286.60i	836.950			−1027.59	−	6268.79i	−8006.43			4874.15	+	8442.27i	11085.4	−	19200.5i
53.16	−3.17713	−	5.50295i	−43.2245	+	74.8670i	235.812	−	408.438i	309.299	+	535.721i	549.319			2332.15	+	5908.87i	−6250.20			6104.79	+	10573.8i	1965.36	−	3404.11i
53.17	1.23518	+	2.13940i	123.516	−	213.936i	252.949	−	438.120i	7.89996	+	13.6831i	610.260			6152.39	+	1581.67i	2514.58			−20671.0	−	35803.2i	−19.5158	+	33.8023i
53.18	3.40903	+	5.90461i	60.0224	−	103.962i	232.757	−	403.147i	−1037.25	−	1796.57i	818.472			−3655.86	+	5195.02i	6664.75			2636.12	+	4565.90i	7072.05	−	12249.2i
53.19	3.45631	+	5.98650i	85.5848	−	148.237i	232.108	−	402.023i	432.273	+	748.719i	1183.23			3520.91	−	5287.42i	6748.21			−4808.01	−	8327.72i	−2988.14	+	5175.61i
53.20	3.62786	+	6.28364i	−95.9625	+	166.212i	229.677	−	397.813i	−40.4745	−	70.1038i	−1392.55			−5859.16	−	2454.35i	7047.87			−8576.10	−	14854.2i	293.671	−	508.654i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.c	even	3	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	91.10.e.a	✓	70
7.c	even	3	1	inner	91.10.e.a	✓	70

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
91.10.e.a	✓	70	1.a	even	1	1	trivial
91.10.e.a	✓	70	7.c	even	3	1	inner