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Properties

Label 95.11.f.a
Level $95$
Weight $11$
Character orbit 95.f
Analytic conductor $60.359$
Analytic rank $0$
Dimension $180$
Inner twists $2$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [95,11,Mod(58,95)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3, 0])) N = Newforms(chi, 11, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("95.58"); S:= CuspForms(chi, 11); N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 95.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
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 algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 180 q - 64 q^{2} - 124 q^{3} + 8454 q^{5} - 24320 q^{6} + 32890 q^{7} + 98304 q^{8} + 322576 q^{10} + 435480 q^{11} - 1494224 q^{12} - 48556 q^{13} + 4094384 q^{15} - 44262960 q^{16} - 505646 q^{17} - 6298560 q^{18}+ \cdots - 60964218864 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
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
See next 80 embeddings (of 180 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 58.90
Significant digits:
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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 \(S_{11}^{\mathrm{new}}(95, [\chi])\).