Newform orbit 95.11.f.a

• Label: 95.11.f.a
• Level: $95$
• Weight: $11$
• Character orbit: 95.f
• Analytic conductor: $60.359$
• Analytic rank: $0$
• Dimension: $180$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	95.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(60.3589390040\)
Analytic rank:	\(0\)
Dimension:	\(180\)
Relative dimension:	\(90\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 180 q - 64 q^{2} - 124 q^{3} + 8454 q^{5} - 24320 q^{6} + 32890 q^{7} + 98304 q^{8}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
58.1	−45.1514	+	45.1514i	91.4732	+	91.4732i		−	3053.31i	−1948.11	−	2443.46i	−8260.29			16335.2	−	16335.2i	91626.1	+	91626.1i		−	42314.3i	198286.	+	22365.4i
58.2	−43.4479	+	43.4479i	−264.279	−	264.279i		−	2751.43i	1395.24	−	2796.23i	22964.7			−9540.73	+	9540.73i	75053.3	+	75053.3i			80637.3i	60870.1	+	182111.i
58.3	−42.9293	+	42.9293i	−28.6501	−	28.6501i		−	2661.85i	2263.59	+	2154.48i	2459.86			1738.71	−	1738.71i	70311.8	+	70311.8i		−	57407.3i	−189665.	+	4683.68i
58.4	−41.8993	+	41.8993i	187.251	+	187.251i		−	2487.10i	2598.42	−	1736.04i	−15691.3			−11959.6	+	11959.6i	61302.8	+	61302.8i			11076.5i	−36133.4	+	181611.i
58.5	−41.4391	+	41.4391i	−281.189	−	281.189i		−	2410.40i	−2290.15	+	2126.23i	23304.4			9996.07	−	9996.07i	57451.0	+	57451.0i			99085.7i	6792.86	−	183011.i
58.6	−41.2058	+	41.2058i	−47.8064	−	47.8064i		−	2371.83i	−965.595	+	2972.08i	3939.80			−16541.7	+	16541.7i	55538.5	+	55538.5i		−	54478.1i	−82678.7	−	162255.i
58.7	−40.7156	+	40.7156i	263.750	+	263.750i		−	2291.52i	−3026.15	+	779.765i	−21477.5			−16386.6	+	16386.6i	51607.8	+	51607.8i			80078.9i	91462.9	−	154960.i
58.8	−39.8048	+	39.8048i	271.938	+	271.938i		−	2144.84i	−148.649	+	3121.46i	−21648.9			18156.8	−	18156.8i	44615.0	+	44615.0i			88851.5i	−118332.	−	130166.i
58.9	−38.0420	+	38.0420i	223.920	+	223.920i		−	1870.39i	3123.26	+	104.196i	−17036.7			−872.621	+	872.621i	32198.3	+	32198.3i			41231.4i	−122779.	+	114851.i
58.10	−37.6315	+	37.6315i	−73.9276	−	73.9276i		−	1808.25i	−3060.01	+	634.018i	5564.00			696.011	−	696.011i	29512.6	+	29512.6i		−	48118.4i	91293.5	−	139012.i
58.11	−37.3583	+	37.3583i	−75.2040	−	75.2040i		−	1767.29i	2911.20	+	1136.02i	5618.99			14368.5	−	14368.5i	27768.1	+	27768.1i		−	47737.7i	−151197.	+	66317.7i
58.12	−36.7513	+	36.7513i	−202.747	−	202.747i		−	1677.32i	2165.70	−	2252.86i	14902.4			19694.3	−	19694.3i	24010.4	+	24010.4i			23163.5i	3203.12	+	162388.i
58.13	−36.5520	+	36.5520i	−188.669	−	188.669i		−	1648.10i	−2471.44	−	1912.49i	13792.4			−3293.25	+	3293.25i	22812.0	+	22812.0i			12142.8i	160241.	−	20430.7i
58.14	−35.2241	+	35.2241i	−282.164	−	282.164i		−	1457.48i	2438.43	+	1954.40i	19878.0			−8468.50	+	8468.50i	15268.9	+	15268.9i			100184.i	−154734.	+	17049.4i
58.15	−33.7403	+	33.7403i	307.162	+	307.162i		−	1252.82i	−276.952	−	3112.70i	−20727.5			4504.44	−	4504.44i	7720.32	+	7720.32i			129649.i	114368.	+	95679.1i
58.16	−32.1536	+	32.1536i	141.341	+	141.341i		−	1043.71i	−366.986	+	3103.38i	−9089.22			404.504	−	404.504i	633.739	+	633.739i		−	19094.7i	−87984.8	−	111585.i
58.17	−31.5234	+	31.5234i	77.9845	+	77.9845i		−	963.450i	1793.82	−	2558.87i	−4916.67			9033.25	−	9033.25i	−1908.74	−	1908.74i		−	46885.8i	24117.0	+	137212.i
58.18	−30.9643	+	30.9643i	118.936	+	118.936i		−	893.578i	−3095.07	−	431.480i	−7365.54			11056.7	−	11056.7i	−4038.44	−	4038.44i		−	30757.5i	109197.	−	82476.2i
58.19	−28.2834	+	28.2834i	−132.432	−	132.432i		−	575.896i	2861.11	−	1256.86i	7491.25			−14819.3	+	14819.3i	−12673.9	−	12673.9i		−	23972.4i	−45373.5	+	116470.i
58.20	−27.0389	+	27.0389i	145.189	+	145.189i		−	438.207i	2114.71	+	2300.79i	−7851.52			−16374.3	+	16374.3i	−15839.2	−	15839.2i		−	16889.2i	−119390.	−	5031.30i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	95.11.f.a	✓	180
5.c	odd	4	1	inner	95.11.f.a	✓	180

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
95.11.f.a	✓	180	1.a	even	1	1	trivial
95.11.f.a	✓	180	5.c	odd	4	1	inner

Hecke kernels

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