Newform orbit 95.11.h.a

• Label: 95.11.h.a
• Level: $95$
• Weight: $11$
• Character orbit: 95.h
• Analytic conductor: $60.359$
• Analytic rank: $0$
• Dimension: $196$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	95.h (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(60.3589390040\)
Analytic rank:	\(0\)
Dimension:	\(196\)
Relative dimension:	\(98\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 196 q - 48544 q^{4} - 1112 q^{5} + 6524 q^{6} - 1850204 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
69.1	−31.0972	−	53.8620i	141.463	+	245.021i	−1422.08	+	2463.11i	2370.23	−	2036.58i	8798.20	−	15238.9i		−	24743.9i	113204.			−10498.9	+	18184.6i	−183402.	−	64333.1i
69.2	−30.5593	−	52.9303i	−145.722	−	252.398i	−1355.74	+	2348.22i	−3041.00	+	719.688i	−8906.32	+	15426.2i			6339.92i	103137.			−12945.2	+	22421.7i	131024.	+	138968.i
69.3	−30.1860	−	52.2837i	−44.5939	−	77.2389i	−1310.39	+	2269.66i	−536.928	−	3078.53i	−2692.22	+	4663.07i			1063.31i	96401.0			25547.3	−	44249.2i	−144749.	+	121001.i
69.4	−30.1474	−	52.2168i	183.751	+	318.267i	−1305.73	+	2261.59i	−2287.13	−	2129.47i	11079.3	−	19189.8i			27908.2i	95715.7			−38004.7	+	65826.1i	−42243.0	+	183625.i
69.5	−29.6998	−	51.4415i	38.6395	+	66.9256i	−1252.15	+	2168.79i	−1777.71	+	2570.09i	2295.17	−	3975.35i			3017.28i	87929.4			26538.5	−	45966.0i	185007.	+	15116.7i
69.6	−29.6027	−	51.2733i	−175.958	−	304.768i	−1240.63	+	2148.84i	3075.45	+	554.288i	−10417.6	+	18043.9i			28006.3i	86278.0			−32397.8	+	56114.7i	−62621.3	−	174097.i
69.7	−28.9573	−	50.1555i	−99.3809	−	172.133i	−1165.05	+	2017.93i	2278.49	+	2138.72i	−5755.60	+	9969.00i		−	25373.5i	75642.4			9771.39	−	16924.5i	41289.9	−	176210.i
69.8	−27.2030	−	47.1170i	−214.985	−	372.364i	−968.006	+	1676.64i	498.372	−	3085.00i	−11696.4	+	20258.8i		−	16403.3i	49618.9			−62912.2	+	108967.i	−158913.	+	60439.6i
69.9	−27.1737	−	47.0662i	229.028	+	396.688i	−964.816	+	1671.11i	882.048	+	2997.94i	12447.1	−	21559.0i		−	9710.93i	49218.7			−75383.3	+	130568.i	117133.	−	122980.i
69.10	−26.9081	−	46.6062i	161.496	+	279.720i	−936.091	+	1621.36i	3001.11	−	871.185i	8691.11	−	15053.4i			26377.2i	45645.9			−22637.5	+	39209.3i	−121357.	−	116428.i
69.11	−26.6844	−	46.2187i	−6.98703	−	12.1019i	−912.114	+	1579.83i	2971.32	−	967.934i	−372.889	+	645.863i			7051.48i	42707.2			29426.9	−	50968.8i	−124024.	−	111502.i
69.12	−26.6569	−	46.1711i	90.8504	+	157.358i	−909.179	+	1574.74i	1236.97	+	2869.76i	4843.58	−	8389.32i			6004.35i	42350.2			13016.9	−	22545.9i	99526.1	−	133611.i
69.13	−25.9569	−	44.9586i	134.905	+	233.663i	−835.518	+	1447.16i	−3106.25	−	341.819i	7003.43	−	12130.3i		−	20025.3i	33590.0			−6874.35	+	11906.7i	65260.8	+	148525.i
69.14	−23.6126	−	40.8982i	−82.5829	−	143.038i	−603.111	+	1044.62i	−3123.84	−	85.0498i	−3900.00	+	6754.99i		−	29811.8i	8605.49			15884.6	−	27513.0i	70283.7	+	129768.i
69.15	−23.6124	−	40.8978i	8.67290	+	15.0219i	−603.089	+	1044.58i	−1663.86	−	2645.22i	409.575	−	709.405i			3668.45i	8603.30			29374.1	−	50877.4i	−68896.1	+	130508.i
69.16	−23.3148	−	40.3824i	−199.526	−	345.589i	−575.160	+	996.207i	−582.168	+	3070.29i	−9303.81	+	16114.7i		−	8841.39i	5890.30			−50096.6	+	86769.8i	137559.	−	48073.9i
69.17	−22.9027	−	39.6686i	−186.130	−	322.386i	−537.064	+	930.222i	−2851.95	−	1277.51i	−8525.73	+	14767.0i			18942.0i	2296.10			−39764.0	+	68873.2i	14640.3	+	142391.i
69.18	−22.4656	−	38.9116i	−44.1029	−	76.3884i	−497.410	+	861.540i	579.286	−	3070.84i	−1981.60	+	3432.23i			14758.8i	−1311.06			25634.4	−	44400.0i	−132505.	+	46447.4i
69.19	−21.6887	−	37.5659i	−95.0552	−	164.640i	−428.799	+	742.702i	904.938	+	2991.11i	−4123.25	+	7141.67i			25401.6i	−7218.06			11453.5	−	19838.1i	92736.7	−	98868.0i
69.20	−20.6104	−	35.6982i	208.009	+	360.282i	−337.577	+	584.700i	−985.086	−	2965.68i	8574.29	−	14851.1i			939.631i	−14379.7			−57010.9	+	98745.7i	−85566.4	+	96289.6i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
19.d	odd	6	1	inner
95.h	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	95.11.h.a	✓	196
5.b	even	2	1	inner	95.11.h.a	✓	196
19.d	odd	6	1	inner	95.11.h.a	✓	196
95.h	odd	6	1	inner	95.11.h.a	✓	196

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
95.11.h.a	✓	196	1.a	even	1	1	trivial
95.11.h.a	✓	196	5.b	even	2	1	inner
95.11.h.a	✓	196	19.d	odd	6	1	inner
95.11.h.a	✓	196	95.h	odd	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{11}^{\mathrm{new}}(95, [\chi])\).