Newform orbit 95.11.m.a

• Label: 95.11.m.a
• Level: $95$
• Weight: $11$
• Character orbit: 95.m
• Analytic conductor: $60.359$
• Analytic rank: $0$
• Dimension: $392$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	95.m (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(60.3589390040\)
Analytic rank:	\(0\)
Dimension:	\(392\)
Relative dimension:	\(98\) over \(\Q(\zeta_{12})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 392 q - 2 q^{2} - 2 q^{3} + 2220 q^{5} + 4856 q^{6} + 7780 q^{7} - 142356 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
7.1	−16.0969	+	60.0744i	123.006	+	32.9594i	−2463.02	−	1422.02i	−211.163	−	3117.86i	−3960.03	+	6858.97i	8225.62	+	8225.62i	80041.1	−	80041.1i	−37093.8	−	21416.1i	190703.	+	37502.3i
7.2	−15.7465	+	58.7666i	388.673	+	104.145i	−2318.75	−	1338.73i	−1999.78	+	2401.36i	−12240.4	+	21201.1i	10291.6	+	10291.6i	71132.1	−	71132.1i	89082.5	+	51431.8i	−109630.	−	155333.i
7.3	−15.7051	+	58.6121i	−383.064	−	102.642i	−2301.92	−	1329.02i	896.038	−	2993.78i	12032.1	−	20840.2i	−11158.5	−	11158.5i	70111.4	−	70111.4i	85064.6	+	49112.1i	161400.	+	99536.3i
7.4	−15.6303	+	58.3330i	213.494	+	57.2056i	−2271.63	−	1311.52i	2345.18	+	2065.38i	−6673.95	+	11559.6i	−12299.4	−	12299.4i	68283.7	−	68283.7i	−8830.70	−	5098.41i	−157135.	+	104519.i
7.5	−15.4368	+	57.6108i	−202.636	−	54.2963i	−2193.90	−	1266.65i	3032.06	+	756.447i	6256.10	−	10835.9i	13207.4	+	13207.4i	63653.0	−	63653.0i	−13024.5	−	7519.68i	−90384.7	+	163002.i
7.6	−15.2296	+	56.8375i	−76.4669	−	20.4892i	−2111.75	−	1219.22i	−1708.34	+	2616.72i	2329.12	−	4034.15i	14139.6	+	14139.6i	58852.1	−	58852.1i	−45710.6	−	26391.0i	−122710.	−	136949.i
7.7	−14.8503	+	55.4219i	143.595	+	38.4762i	−1964.25	−	1134.06i	−3040.04	−	723.714i	−4264.85	+	7386.94i	−18580.5	−	18580.5i	50476.0	−	50476.0i	−31998.7	−	18474.5i	85255.1	−	157738.i
7.8	−14.5104	+	54.1536i	−304.466	−	81.5815i	−1835.25	−	1059.58i	415.173	+	3097.30i	8835.86	−	15304.2i	−19458.5	−	19458.5i	43415.6	−	43415.6i	34906.3	+	20153.2i	−173754.	−	22459.9i
7.9	−14.4462	+	53.9139i	−259.520	−	69.5381i	−1811.20	−	1045.70i	−3015.66	−	819.415i	7498.14	−	12987.2i	−366.409	−	366.409i	42127.8	−	42127.8i	11377.0	+	6568.54i	87742.6	−	150748.i
7.10	−13.5993	+	50.7533i	410.062	+	109.876i	−1504.15	−	868.420i	1812.79	−	2545.47i	−11153.1	+	19317.8i	−7833.14	−	7833.14i	26484.9	−	26484.9i	104940.	+	60587.2i	104538.	+	126622.i
7.11	−13.3807	+	49.9376i	47.8041	+	12.8091i	−1427.91	−	824.405i	2760.52	−	1464.63i	−1279.31	+	2215.83i	−9929.92	−	9929.92i	22841.1	−	22841.1i	−49016.8	−	28299.8i	36202.1	+	157452.i
7.12	−12.8353	+	47.9020i	337.958	+	90.5556i	−1243.04	−	717.671i	2913.63	+	1129.76i	−8675.58	+	15026.5i	20232.3	+	20232.3i	14424.4	−	14424.4i	54877.4	+	31683.5i	−91515.1	+	125068.i
7.13	−12.5417	+	46.8064i	−107.569	−	28.8232i	−1146.74	−	662.069i	2321.76	−	2091.66i	2698.22	−	4673.45i	4809.27	+	4809.27i	10284.1	−	10284.1i	−40397.5	−	23323.5i	68784.1	+	134907.i
7.14	−12.4652	+	46.5207i	325.085	+	87.1063i	−1121.98	−	647.777i	−2409.61	−	1989.82i	−8104.49	+	14037.4i	8414.06	+	8414.06i	9247.91	−	9247.91i	46954.8	+	27109.4i	122604.	−	87293.3i
7.15	−12.3979	+	46.2697i	−443.419	−	118.814i	−1100.37	−	635.297i	−850.116	+	3007.15i	10995.0	−	19043.8i	11578.3	+	11578.3i	8352.55	−	8352.55i	131366.	+	75844.1i	−128600.	−	76617.0i
7.16	−12.1090	+	45.1916i	62.4601	+	16.7361i	−1008.84	−	582.454i	−1109.16	−	2921.54i	−1512.66	+	2620.01i	16010.4	+	16010.4i	4661.56	−	4661.56i	−47516.8	−	27433.8i	145460.	−	14747.5i
7.17	−11.6784	+	43.5845i	29.8802	+	8.00639i	−876.413	−	505.997i	−2369.61	+	2037.30i	−697.909	+	1208.81i	−349.071	−	349.071i	−383.062	+	383.062i	−50309.2	−	29046.0i	−61121.4	−	127071.i
7.18	−11.5840	+	43.2320i	−420.625	−	112.706i	−848.005	−	489.596i	471.452	−	3089.23i	9745.02	−	16878.9i	19755.7	+	19755.7i	−1418.10	+	1418.10i	113085.	+	65289.7i	128092.	+	56167.4i
7.19	−11.5704	+	43.1812i	28.4153	+	7.61384i	−843.934	−	487.246i	81.7868	+	3123.93i	−657.550	+	1138.91i	−7638.87	−	7638.87i	−1565.02	+	1565.02i	−50388.5	−	29091.8i	−135841.	−	32613.4i
7.20	−11.3887	+	42.5031i	182.520	+	48.9060i	−790.000	−	456.107i	1136.08	+	2911.18i	−4157.31	+	7200.67i	4854.66	+	4854.66i	−3478.16	+	3478.16i	−20216.3	−	11671.9i	−136672.	+	15132.3i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
19.c	even	3	1	inner
95.m	odd	12	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	95.11.m.a	✓	392
5.c	odd	4	1	inner	95.11.m.a	✓	392
19.c	even	3	1	inner	95.11.m.a	✓	392
95.m	odd	12	1	inner	95.11.m.a	✓	392

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
95.11.m.a	✓	392	1.a	even	1	1	trivial
95.11.m.a	✓	392	5.c	odd	4	1	inner
95.11.m.a	✓	392	19.c	even	3	1	inner
95.11.m.a	✓	392	95.m	odd	12	1	inner

Hecke kernels

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