Newform orbit 91.5.y.a

• Label: 91.5.y.a
• Level: $91$
• Weight: $5$
• Character orbit: 91.y
• Analytic conductor: $9.407$
• Analytic rank: $0$
• Dimension: $112$
• Inner twists: $2$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(9.40666664063\)
Analytic rank:	\(0\)
Dimension:	\(112\)
Relative dimension:	\(28\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 112 q - 24 q^{5} + 132 q^{6} - 252 q^{8} - 1512 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
15.1	−7.48429	−	2.00541i	−4.04472	−	7.00566i	38.1365	+	22.0181i	−12.4817	+	12.4817i	16.2226	+	60.5437i	17.8892	−	4.79340i	−153.607	−	153.607i	7.78053	−	13.4763i	118.448	−	68.3860i
15.2	−6.77988	−	1.81666i	2.64324	+	4.57823i	28.8102	+	16.6336i	10.3095	−	10.3095i	−9.60378	−	35.8418i	17.8892	−	4.79340i	−85.7005	−	85.7005i	26.5265	−	45.9453i	−88.6258	+	51.1681i
15.3	−6.32886	−	1.69581i	−1.18264	−	2.04839i	23.3223	+	13.4651i	−1.49650	+	1.49650i	4.01107	+	14.9695i	−17.8892	+	4.79340i	−50.6405	−	50.6405i	37.7027	−	65.3031i	12.0090	−	6.93338i
15.4	−6.29214	−	1.68597i	5.59104	+	9.68397i	22.8922	+	13.2168i	35.2136	−	35.2136i	−18.8527	−	70.3593i	−17.8892	+	4.79340i	−48.0589	−	48.0589i	−22.0196	+	38.1390i	−280.939	+	162.200i
15.5	−6.26332	−	1.67825i	−7.57425	−	13.1190i	22.5562	+	13.0228i	19.7636	−	19.7636i	25.4230	+	94.8798i	−17.8892	+	4.79340i	−46.0601	−	46.0601i	−74.2384	+	128.585i	−156.954	+	90.6174i
15.6	−4.85396	−	1.30062i	−0.985675	−	1.70724i	8.01295	+	4.62628i	−31.1904	+	31.1904i	2.56397	+	9.56886i	−17.8892	+	4.79340i	23.9760	+	23.9760i	38.5569	−	66.7825i	191.964	−	110.830i
15.7	−4.53284	−	1.21457i	−7.94599	−	13.7629i	5.21509	+	3.01093i	−19.3441	+	19.3441i	19.3019	+	72.0358i	17.8892	−	4.79340i	33.1102	+	33.1102i	−85.7774	+	148.571i	111.179	−	64.1890i
15.8	−4.11478	−	1.10255i	4.12647	+	7.14726i	1.85941	+	1.07353i	−1.49291	+	1.49291i	−9.09931	−	33.9591i	17.8892	−	4.79340i	41.7282	+	41.7282i	6.44444	−	11.1621i	7.78901	−	4.49699i
15.9	−3.93225	−	1.05364i	−1.90652	−	3.30219i	0.496049	+	0.286394i	19.0688	−	19.0688i	4.01759	+	14.9939i	17.8892	−	4.79340i	44.4089	+	44.4089i	33.2304	−	57.5567i	−95.0753	+	54.8917i
15.10	−2.71417	−	0.727259i	7.55128	+	13.0792i	−7.01860	−	4.05219i	−0.582134	+	0.582134i	−10.9835	−	40.9909i	−17.8892	+	4.79340i	47.8932	+	47.8932i	−73.5436	+	127.381i	2.00337	−	1.15665i
15.11	−2.09499	−	0.561350i	2.63630	+	4.56621i	−9.78255	−	5.64796i	2.05589	−	2.05589i	−2.95978	−	11.0460i	−17.8892	+	4.79340i	41.8620	+	41.8620i	26.5998	−	46.0722i	−5.46114	+	3.15299i
15.12	−1.15507	−	0.309500i	2.35620	+	4.08106i	−12.6180	−	7.28501i	−29.6528	+	29.6528i	−1.45849	−	5.44317i	17.8892	−	4.79340i	25.8491	+	25.8491i	29.3966	−	50.9164i	43.4287	−	25.0735i
15.13	−0.544732	−	0.145961i	−2.95616	−	5.12022i	−13.5810	−	7.84098i	31.2161	−	31.2161i	0.862965	+	3.22063i	−17.8892	+	4.79340i	12.6339	+	12.6339i	23.0223	−	39.8757i	−21.5607	+	12.4481i
15.14	−0.244358	−	0.0654755i	−6.10406	−	10.5725i	−13.8010	−	7.96800i	−15.5864	+	15.5864i	0.799333	+	2.98315i	−17.8892	+	4.79340i	5.71279	+	5.71279i	−34.0191	+	58.9228i	4.82917	−	2.78812i
15.15	−0.219656	−	0.0588566i	5.98329	+	10.3634i	−13.8116	−	7.97414i	26.3459	−	26.3459i	−0.704312	−	2.62853i	17.8892	−	4.79340i	5.13726	+	5.13726i	−31.0994	+	53.8658i	−7.33767	+	4.23640i
15.16	0.455575	+	0.122071i	−3.69943	−	6.40760i	−13.6638	−	7.88878i	−8.56058	+	8.56058i	−0.903186	−	3.37074i	17.8892	−	4.79340i	−10.5979	−	10.5979i	13.1284	−	22.7391i	−4.94498	+	2.85499i
15.17	1.92597	+	0.516062i	7.99140	+	13.8415i	−10.4134	−	6.01216i	−14.2080	+	14.2080i	8.24812	+	30.7824i	17.8892	−	4.79340i	−39.5117	−	39.5117i	−87.2249	+	151.078i	−34.6965	+	20.0320i
15.18	1.99770	+	0.535283i	−8.78280	−	15.2123i	−10.1521	−	5.86133i	26.5980	−	26.5980i	−9.40257	−	35.0909i	17.8892	−	4.79340i	−40.5422	−	40.5422i	−113.775	+	197.065i	67.3723	−	38.8974i
15.19	2.22041	+	0.594958i	1.11959	+	1.93919i	−9.28015	−	5.35790i	−5.87167	+	5.87167i	1.33222	+	4.97191i	−17.8892	+	4.79340i	−43.4253	−	43.4253i	37.9930	−	65.8059i	−16.5309	+	9.54413i
15.20	3.65151	+	0.978420i	4.24787	+	7.35753i	−1.48017	−	0.854576i	−27.1569	+	27.1569i	8.31241	+	31.0223i	−17.8892	+	4.79340i	−47.3382	−	47.3382i	4.41112	−	7.64028i	−125.735	+	72.5929i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
13.f	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.y.a	✓	112
13.f	odd	12	1	inner	91.5.y.a	✓	112

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
91.5.y.a	✓	112	1.a	even	1	1	trivial
91.5.y.a	✓	112	13.f	odd	12	1	inner

Hecke kernels

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