Newform orbit 91.5.l.a

• Label: 91.5.l.a
• Level: $91$
• Weight: $5$
• Character orbit: 91.l
• Analytic conductor: $9.407$
• Analytic rank: $0$
• Dimension: $70$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	91.l (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(9.40666664063\)
Analytic rank:	\(0\)
Dimension:	\(70\)
Relative dimension:	\(35\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 70 q - 12 q^{3} - 514 q^{4} - 35 q^{7} + 777 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
17.1		−	7.51974i	−3.00815	+	1.73675i	−40.5464			6.92948	+	12.0022i	13.0599	+	22.6205i	38.0681	+	30.8516i			184.583i	−34.4674	+	59.6992i	90.2535	−	52.1079i
17.2		−	7.39124i	9.80915	−	5.66332i	−38.6305			4.05763	+	7.02801i	−41.8590	−	72.5018i	−33.5445	−	35.7178i			167.267i	23.6463	−	40.9567i	51.9458	−	29.9909i
17.3		−	7.38104i	−10.1867	+	5.88130i	−38.4797			−18.7095	−	32.4057i	43.4101	+	75.1884i	−38.8079	−	29.9157i			165.924i	28.6793	−	49.6739i	−239.188	+	138.095i
17.4		−	6.37781i	9.19534	−	5.30893i	−24.6764			−19.6111	−	33.9675i	−33.8593	−	58.6461i	48.8654	−	3.62887i			55.3366i	15.8695	−	27.4868i	−216.638	+	125.076i
17.5		−	6.14692i	−0.430586	+	0.248599i	−21.7847			4.14143	+	7.17316i	1.52812	+	2.64678i	−28.6157	+	39.7762i			35.5579i	−40.3764	+	69.9340i	44.0929	−	25.4570i
17.6		−	5.90642i	−12.7056	+	7.33559i	−18.8858			8.30387	+	14.3827i	43.3271	+	75.0447i	48.3671	−	7.85001i			17.0446i	67.1218	−	116.258i	84.9504	−	49.0461i
17.7		−	5.36897i	3.59668	−	2.07654i	−12.8259			24.1866	+	41.8925i	−11.1489	−	19.3104i	9.08174	−	48.1510i		−	17.0419i	−31.8759	+	55.2108i	224.920	−	129.857i
17.8		−	4.72938i	13.5621	−	7.83009i	−6.36704			12.9537	+	22.4364i	−37.0315	−	64.1404i	33.6198	+	35.6470i		−	45.5579i	82.1205	−	142.237i	106.110	−	61.2629i
17.9		−	4.64672i	−4.49413	+	2.59469i	−5.59198			−5.55653	−	9.62418i	12.0568	+	20.8830i	8.58872	−	48.2414i		−	48.3631i	−27.0352	+	46.8263i	−44.7209	+	25.8196i
17.10		−	4.43931i	−12.7917	+	7.38530i	−3.70745			8.64271	+	14.9696i	32.7856	+	56.7863i	−40.3891	+	27.7438i		−	54.5704i	68.5853	−	118.793i	66.4547	−	38.3677i
17.11		−	4.35221i	5.32630	−	3.07514i	−2.94171			−15.7477	−	27.2758i	−13.3836	−	23.1812i	−38.7103	+	30.0419i		−	56.8324i	−21.5870	+	37.3898i	−118.710	+	68.5371i
17.12		−	2.63512i	11.8563	−	6.84523i	9.05614			0.577845	+	1.00086i	−18.0380	−	31.2427i	−46.8363	−	14.3999i		−	66.0260i	53.2143	−	92.1699i	2.63738	−	1.52269i
17.13		−	2.54803i	−11.5386	+	6.66183i	9.50754			−22.1587	−	38.3800i	16.9745	+	29.4008i	13.7758	+	47.0237i		−	64.9940i	48.2600	−	83.5887i	−97.7933	+	56.4610i
17.14		−	2.18884i	−1.46861	+	0.847902i	11.2090			−7.17402	−	12.4258i	1.85592	+	3.21456i	48.5687	+	6.48733i		−	59.5562i	−39.0621	+	67.6576i	−27.1981	+	15.7028i
17.15		−	1.84585i	−4.73814	+	2.73557i	12.5928			20.5363	+	35.5700i	5.04946	+	8.74591i	−47.5693	−	11.7541i		−	52.7781i	−25.5333	+	44.2250i	65.6570	−	37.9071i
17.16		−	1.14906i	3.07860	−	1.77743i	14.6796			12.6929	+	21.9847i	−2.04239	−	3.53752i	18.4219	+	45.4052i		−	35.2529i	−34.1815	+	59.2040i	25.2619	−	14.5850i
17.17		−	1.10958i	9.89188	−	5.71108i	14.7688			−7.23606	−	12.5332i	−6.33691	−	10.9759i	14.2396	−	46.8853i		−	34.1405i	24.7329	−	42.8386i	−13.9066	+	8.02901i
17.18		−	0.155902i	−8.89060	+	5.13299i	15.9757			−3.98714	−	6.90593i	0.800243	+	1.38606i	−29.3293	−	39.2530i		−	4.98507i	12.1952	−	21.1227i	−1.07665	+	0.621603i
17.19			0.882988i	−11.6628	+	6.73354i	15.2203			15.5807	+	26.9865i	−5.94564	−	10.2981i	45.7112	−	17.6490i			27.5672i	50.1811	−	86.9162i	−23.8288	+	13.7575i
17.20			1.34745i	0.0968361	−	0.0559084i	14.1844			−21.2700	−	36.8407i	0.0753336	+	0.130482i	−46.4342	−	15.6483i			40.6719i	−40.4937	+	70.1372i	49.6410	−	28.6602i

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	91.5.l.a	✓	70
7.d	odd	6	1		91.5.p.a	yes	70
13.e	even	6	1		91.5.p.a	yes	70
91.l	odd	6	1	inner	91.5.l.a	✓	70

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
91.5.l.a	✓	70	1.a	even	1	1	trivial
91.5.l.a	✓	70	91.l	odd	6	1	inner
91.5.p.a	yes	70	7.d	odd	6	1
91.5.p.a	yes	70	13.e	even	6	1

Hecke kernels

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