Newform orbit 95.11.o.a

• Label: 95.11.o.a
• Level: $95$
• Weight: $11$
• Character orbit: 95.o
• Analytic conductor: $60.359$
• Analytic rank: $0$
• Dimension: $588$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	95.o (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(60.3589390040\)
Analytic rank:	\(0\)
Dimension:	\(588\)
Relative dimension:	\(98\) over \(\Q(\zeta_{18})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 588 q - 1842 q^{4} - 6 q^{5} - 7302 q^{6} - 12 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
14.1	−60.0818	+	21.8680i	−57.8803	+	328.256i	2347.19	−	1969.52i	3025.95	+	780.555i	−3700.74	−	20987.9i	−15063.3	+	8696.78i	−65217.5	+	112960.i	−48913.8	−	17803.2i	−198874.	+	19274.3i
14.2	−58.7309	+	21.3763i	77.9277	−	441.950i	2207.94	−	1852.68i	−3124.89	−	26.5577i	4870.49	+	27621.9i	4083.93	−	2357.86i	−58070.7	+	100581.i	−133759.	−	48684.3i	184095.	−	65238.7i
14.3	−56.6254	+	20.6100i	29.8981	−	169.560i	1997.24	−	1675.88i	2870.07	−	1236.26i	1801.64	+	10217.6i	18208.5	−	10512.7i	−47701.8	+	82622.0i	27631.1	+	10056.9i	−137040.	+	129156.i
14.4	−56.5359	+	20.5774i	7.49325	−	42.4964i	1988.45	−	1668.50i	−1014.68	−	2955.68i	450.826	+	2556.76i	−12222.5	+	7056.68i	−47281.0	+	81893.1i	53738.1	+	19559.1i	118186.	+	146223.i
14.5	−55.5010	+	20.2007i	−66.6891	+	378.213i	1887.87	−	1584.11i	−3012.75	−	830.042i	−3938.86	−	22338.4i	282.737	−	163.238i	−42538.2	+	73678.3i	−83109.4	−	30249.4i	183978.	−	14791.5i
14.6	−54.6793	+	19.9017i	−24.3306	+	137.986i	1809.33	−	1518.20i	−445.628	+	3093.06i	−1415.76	−	8029.19i	6642.36	−	3834.97i	−38925.4	+	67420.8i	37039.8	+	13481.4i	−37190.4	−	177995.i
14.7	−54.3413	+	19.7786i	31.4181	−	178.181i	1777.35	−	1491.38i	165.517	+	3120.61i	1816.87	+	10304.0i	9291.27	−	5364.32i	−37477.9	+	64913.6i	24726.6	+	8999.73i	−70715.8	−	166304.i
14.8	−52.0045	+	18.9281i	−9.70442	+	55.0365i	1561.77	−	1310.48i	−2404.05	−	1996.53i	−537.062	−	3045.83i	24992.6	−	14429.5i	−28079.0	+	48634.2i	52553.1	+	19127.8i	162812.	+	58324.6i
14.9	−51.0497	+	18.5806i	46.5101	−	263.772i	1476.40	−	1238.85i	2310.54	+	2104.05i	2526.71	+	14329.7i	−11690.5	+	6749.50i	−24536.5	+	42498.5i	−11924.6	−	4340.21i	−157047.	−	64480.0i
14.10	−50.4477	+	18.3614i	8.30012	−	47.0723i	1423.39	−	1194.37i	−2581.11	+	1761.68i	445.594	+	2527.09i	−27105.4	+	15649.3i	−22389.7	+	38780.1i	53341.0	+	19414.5i	97863.8	−	136265.i
14.11	−49.5545	+	18.0364i	72.1457	−	409.159i	1345.91	−	1129.35i	2734.31	−	1513.00i	3804.59	+	21576.9i	−14159.9	+	8175.21i	−19326.2	+	33474.0i	−106718.	−	38842.1i	−108208.	+	124293.i
14.12	−48.4927	+	17.6499i	−50.5569	+	286.723i	1255.59	−	1053.57i	−2510.27	+	1861.23i	−2608.98	−	14796.3i	1004.07	−	579.697i	−15869.9	+	27487.5i	−24165.9	−	8795.67i	88879.3	−	134562.i
14.13	−47.3075	+	17.2185i	−28.4010	+	161.070i	1157.09	−	970.917i	2701.98	−	1570.00i	−1429.81	−	8108.85i	9830.11	−	5675.41i	−12245.5	+	21209.9i	30351.0	+	11046.8i	−100791.	+	120797.i
14.14	−47.0573	+	17.1275i	−23.4653	+	133.078i	1136.61	−	953.731i	1823.26	−	2537.98i	−1175.08	−	6664.22i	−14012.0	+	8089.82i	−11511.3	+	19938.2i	38328.6	+	13950.5i	−42328.3	+	150658.i
14.15	−45.2762	+	16.4792i	−64.0259	+	363.109i	993.941	−	834.015i	2685.52	+	1598.00i	−3084.89	−	17495.3i	27021.6	−	15600.9i	−6588.82	+	11412.2i	−72260.9	−	26300.8i	−147924.	−	28096.0i
14.16	−44.7155	+	16.2751i	−69.6806	+	395.179i	950.164	−	797.283i	292.669	−	3111.27i	−3315.77	−	18804.7i	431.688	−	249.235i	−5147.57	+	8915.85i	−95822.8	−	34876.6i	37549.3	+	143885.i
14.17	−43.4596	+	15.8180i	48.3680	−	274.309i	854.096	−	716.672i	−3007.27	+	849.673i	2236.96	+	12686.4i	−798.679	+	461.118i	−2103.00	+	3642.50i	−17417.9	−	6339.58i	117255.	−	84495.4i
14.18	−43.0116	+	15.6549i	40.6903	−	230.766i	820.488	−	688.472i	−1284.24	−	2848.92i	1862.47	+	10562.6i	−9704.24	+	5602.75i	−1077.28	+	1865.91i	3890.60	+	1416.06i	99836.7	+	102432.i
14.19	−39.9647	+	14.5460i	63.6154	−	360.781i	601.166	−	504.438i	142.147	−	3121.77i	2705.54	+	15343.9i	18046.6	−	10419.2i	5087.26	−	8811.39i	−70628.0	−	25706.5i	39728.3	+	126828.i
14.20	−39.5911	+	14.4100i	−31.6778	+	179.654i	575.376	−	482.798i	2283.06	+	2133.84i	−1334.65	−	7569.16i	−23263.4	+	13431.1i	5748.90	−	9957.38i	24215.9	+	8813.87i	−121137.	−	51582.4i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
19.f	odd	18	1	inner
95.o	odd	18	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	95.11.o.a	✓	588
5.b	even	2	1	inner	95.11.o.a	✓	588
19.f	odd	18	1	inner	95.11.o.a	✓	588
95.o	odd	18	1	inner	95.11.o.a	✓	588

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
95.11.o.a	✓	588	1.a	even	1	1	trivial
95.11.o.a	✓	588	5.b	even	2	1	inner
95.11.o.a	✓	588	19.f	odd	18	1	inner
95.11.o.a	✓	588	95.o	odd	18	1	inner

Hecke kernels

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