Newform orbit 89.10.e.a

• Label: 89.10.e.a
• Level: $89$
• Weight: $10$
• Character orbit: 89.e
• Analytic conductor: $45.838$
• Analytic rank: $0$
• Dimension: $660$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 89 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	89.e (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(45.8381894186\)
Analytic rank:	\(0\)
Dimension:	\(660\)
Relative dimension:	\(66\) over \(\Q(\zeta_{11})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 660 q + 23 q^{2} + 803 q^{3} - 16393 q^{4} + 557 q^{5} - 6569 q^{6} - 9 q^{7} + 25591 q^{8} - 324029 q^{9}+O(q^{10}) \)

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	−41.5874	+	12.2112i	−91.5410	−	58.8298i	1149.68	−	738.852i	−465.881	+	537.655i	4525.33	+	1328.76i	−3265.39	+	3768.46i	−24257.3	+	27994.5i	−3257.81	−	7133.60i	12809.4	−	28048.6i
2.2	−40.3542	+	11.8491i	110.510	+	71.0205i	1057.34	−	679.510i	1151.22	−	1328.58i	−5301.07	−	1556.53i	−6522.61	+	7527.50i	−20515.0	+	23675.5i	−1008.06	−	2207.35i	−30714.1	+	67254.5i
2.3	−40.1443	+	11.7874i	42.8610	+	27.5451i	1041.90	−	669.588i	−1220.22	+	1408.21i	−2045.31	−	600.558i	4806.29	−	5546.76i	−19905.4	+	22972.1i	−7098.28	−	15543.1i	32385.6	−	70914.6i
2.4	−39.0605	+	11.4692i	218.188	+	140.221i	963.459	−	619.177i	−186.216	+	214.905i	−10130.8	−	2974.66i	2250.11	−	2596.77i	−16882.3	+	19483.2i	19767.6	+	43284.9i	4808.91	−	10530.1i
2.5	−38.3847	+	11.2708i	−144.173	−	92.6546i	915.633	−	588.441i	1046.91	−	1208.20i	6578.34	+	1931.58i	4480.24	−	5170.48i	−15100.8	+	17427.3i	4024.48	+	8812.38i	−26568.0	+	58175.8i
2.6	−37.8508	+	11.1140i	70.2696	+	45.1595i	878.442	−	564.540i	606.976	−	700.487i	−3161.67	−	928.349i	4184.97	−	4829.71i	−13748.7	+	15866.9i	−5278.18	−	11557.6i	−15189.3	+	33259.9i
2.7	−35.7144	+	10.4867i	108.618	+	69.8043i	734.828	−	472.245i	−1625.55	+	1875.99i	−4611.23	−	1353.98i	−2119.02	+	2445.48i	−8811.47	+	10169.0i	−1251.47	−	2740.33i	38382.8	−	84046.6i
2.8	−34.6520	+	10.1747i	−186.652	−	119.954i	666.514	−	428.342i	−816.098	+	941.827i	7688.38	+	2257.51i	3670.66	−	4236.17i	−6628.84	+	7650.09i	12273.5	+	26875.2i	18696.6	−	40939.8i
2.9	−34.5388	+	10.1415i	−223.343	−	143.534i	659.360	−	423.745i	663.027	−	765.173i	9169.66	+	2692.46i	−7613.74	+	8786.72i	−6406.73	+	7393.76i	21103.5	+	46210.3i	−15140.2	+	33152.3i
2.10	−31.0050	+	9.10389i	−148.307	−	95.3111i	447.708	−	287.725i	−1288.34	+	1486.82i	5465.96	+	1604.95i	2366.97	−	2731.63i	−427.285	+	493.113i	4734.13	+	10366.3i	26409.0	−	57827.7i
2.11	−30.5231	+	8.96240i	8.09598	+	5.20297i	420.615	−	270.313i	1023.65	−	1181.35i	−293.746	−	86.2516i	236.455	−	272.883i	250.282	−	288.840i	−8138.14	−	17820.0i	−20657.1	+	45232.8i
2.12	−29.6680	+	8.71132i	1.06917	+	0.687114i	373.583	−	240.087i	−694.596	+	801.607i	−37.7059	−	11.0714i	−5566.24	+	6423.79i	1375.32	−	1587.20i	−8175.94	−	17902.8i	13624.2	−	29832.9i
2.13	−29.1983	+	8.57340i	−56.8476	−	36.5337i	348.317	−	223.850i	−228.796	+	264.044i	1973.07	+	579.346i	−3142.83	+	3627.02i	1952.04	−	2252.77i	−6279.68	−	13750.6i	4416.69	−	9671.21i
2.14	−28.3523	+	8.32499i	−77.0138	−	49.4938i	303.827	−	195.258i	1593.60	−	1839.11i	2595.56	+	762.124i	−808.567	+	933.136i	2918.86	−	3368.55i	−4695.12	−	10280.9i	−29871.6	+	65409.7i
2.15	−27.7719	+	8.15458i	186.939	+	120.138i	274.062	−	176.129i	−626.266	+	722.750i	−6171.34	−	1812.07i	−5091.25	+	5875.62i	3529.76	−	4073.56i	12336.4	+	27012.9i	11498.9	−	25179.1i
2.16	−26.9859	+	7.92377i	158.835	+	102.077i	234.729	−	150.851i	288.720	−	333.200i	−5095.12	−	1496.06i	−21.2659	+	24.5421i	4290.98	−	4952.06i	6632.16	+	14522.4i	−5151.15	+	11279.4i
2.17	−24.3050	+	7.13661i	179.910	+	115.621i	109.082	−	70.1030i	1548.84	−	1787.46i	−5197.85	−	1526.23i	6628.57	−	7649.78i	6342.29	−	7319.39i	10822.7	+	23698.4i	−24888.3	+	54497.8i
2.18	−23.7265	+	6.96673i	73.9685	+	47.5366i	83.6898	−	53.7842i	−758.384	+	875.222i	−2086.19	−	612.560i	5410.17	−	6243.67i	6680.11	−	7709.26i	−4965.01	−	10871.9i	11896.4	−	26049.4i
2.19	−21.5980	+	6.34176i	−19.4189	−	12.4798i	−4.46459	+	2.86922i	−449.398	+	518.633i	498.554	+	146.389i	7313.21	−	8439.90i	7625.53	−	8800.33i	−7955.26	−	17419.6i	6417.07	−	14051.4i
2.20	−18.7846	+	5.51566i	−116.216	−	74.6874i	−108.283	+	69.5892i	678.802	−	783.379i	2595.02	+	761.966i	−3891.91	+	4491.51i	8214.38	−	9479.90i	−248.702	−	544.582i	−8430.18	+	18459.5i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
89.e	even	11	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	89.10.e.a	✓	660
89.e	even	11	1	inner	89.10.e.a	✓	660

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
89.10.e.a	✓	660	1.a	even	1	1	trivial
89.10.e.a	✓	660	89.e	even	11	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{10}^{\mathrm{new}}(89, [\chi])\).