Properties

Label 95.4.r.a
Level $95$
Weight $4$
Character orbit 95.r
Analytic conductor $5.605$
Analytic rank $0$
Dimension $336$
Inner twists $4$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [95,4,Mod(2,95)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma:// Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("95.2"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([9, 2])) N = Newforms(chi, 4, names="a")
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 95.r (of order \(36\), degree \(12\), 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: \(5.60518145055\)
Analytic rank: \(0\)
Dimension: \(336\)
Relative dimension: \(28\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 336 q - 12 q^{2} - 12 q^{3} - 12 q^{5} + 12 q^{6} + 6 q^{7} - 18 q^{8} - 12 q^{10} - 12 q^{11} - 18 q^{12} - 12 q^{13} - 264 q^{15} - 996 q^{16} + 132 q^{17} + 1116 q^{20} - 600 q^{21} + 468 q^{22} + 564 q^{23}+ \cdots + 1290 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2.1 −3.17544 − 4.53500i −0.205763 − 2.35188i −7.74662 + 21.2837i 7.01527 + 8.70551i −10.0124 + 8.40139i 2.07008 − 7.72564i 78.3396 − 20.9910i 21.1008 − 3.72064i 17.2029 − 59.4580i
2.2 −3.06182 − 4.37273i 0.801228 + 9.15807i −7.00989 + 19.2595i 1.85709 − 11.0250i 37.5926 − 31.5439i −1.04807 + 3.91145i 64.4299 − 17.2639i −56.6385 + 9.98690i −53.8956 + 25.6361i
2.3 −2.70630 − 3.86500i −0.855559 − 9.77909i −4.87798 + 13.4021i 0.171615 − 11.1790i −35.4807 + 29.7719i 0.905101 − 3.37788i 28.5404 − 7.64737i −68.3088 + 12.0447i −43.6713 + 29.5905i
2.4 −2.57053 − 3.67110i −0.0919918 − 1.05147i −4.13318 + 11.3558i −10.0044 − 4.99122i −3.62359 + 3.04055i −3.16174 + 11.7998i 17.6818 − 4.73784i 25.4927 − 4.49505i 7.39334 + 49.5572i
2.5 −2.47264 − 3.53129i 0.343809 + 3.92975i −3.61992 + 9.94565i −9.75843 + 5.45647i 13.0270 − 10.9309i 1.83448 − 6.84636i 10.7596 − 2.88302i 11.2651 − 1.98633i 43.3974 + 20.9680i
2.6 −2.17048 − 3.09977i −0.0734001 − 0.838967i −2.16143 + 5.93847i 10.3606 − 4.20218i −2.44129 + 2.04849i 4.69640 − 17.5272i −6.14222 + 1.64580i 25.8913 − 4.56534i −35.5133 − 22.9947i
2.7 −1.99889 − 2.85471i −0.595193 − 6.80308i −1.41766 + 3.89499i 0.600619 + 11.1642i −18.2311 + 15.2977i −8.87294 + 33.1143i −12.9769 + 3.47715i −19.3379 + 3.40979i 30.6700 − 24.0306i
2.8 −1.81417 − 2.59090i 0.732187 + 8.36894i −0.685394 + 1.88311i 3.89239 + 10.4809i 20.3548 − 17.0797i 4.35988 − 16.2713i −18.3187 + 4.90848i −42.9132 + 7.56676i 20.0935 − 29.0989i
2.9 −1.70511 − 2.43515i 0.362927 + 4.14828i −0.286389 + 0.786848i 10.5574 − 3.67977i 9.48284 − 7.95705i −7.92428 + 29.5738i −20.5674 + 5.51101i 9.51331 − 1.67745i −26.9624 − 19.4345i
2.10 −1.39619 − 1.99397i −0.603385 − 6.89673i 0.709596 − 1.94960i −7.97929 + 7.83141i −12.9094 + 10.8323i 8.58104 − 32.0249i −23.6882 + 6.34722i −20.6110 + 3.63427i 26.7562 + 4.97632i
2.11 −0.867729 − 1.23924i −0.319403 − 3.65079i 1.95339 − 5.36688i −3.62085 − 10.5778i −4.24707 + 3.56372i −0.716622 + 2.67447i −20.0362 + 5.36869i 13.3635 − 2.35635i −9.96655 + 13.6658i
2.12 −0.737954 − 1.05391i 0.528497 + 6.04075i 2.17002 − 5.96207i −10.9602 + 2.20776i 5.97638 − 5.01478i −3.75768 + 14.0239i −17.8268 + 4.77668i −9.62148 + 1.69653i 10.4149 + 9.92180i
2.13 −0.555654 − 0.793556i 0.639977 + 7.31497i 2.41518 − 6.63566i −2.22293 − 10.9571i 5.44923 − 4.57245i 3.52152 − 13.1425i −14.0937 + 3.77640i −26.5094 + 4.67433i −7.45991 + 7.85238i
2.14 −0.382479 − 0.546236i −0.0141242 − 0.161440i 2.58408 − 7.09969i 5.04018 + 9.97981i −0.0827821 + 0.0694624i 1.96157 − 7.32067i −10.0193 + 2.68467i 26.5639 − 4.68394i 3.52357 − 6.57020i
2.15 0.0684753 + 0.0977928i −0.662504 − 7.57246i 2.73129 − 7.50415i 10.9755 − 2.13048i 0.695167 − 0.583314i −0.691001 + 2.57885i 1.84340 − 0.493937i −30.3134 + 5.34507i 0.959894 + 0.927437i
2.16 0.679956 + 0.971077i 0.0660396 + 0.754836i 2.25551 − 6.19696i −4.41803 + 10.2704i −0.688100 + 0.577385i −6.89475 + 25.7315i 16.7120 − 4.47795i 26.0244 − 4.58880i −12.9774 + 2.69316i
2.17 0.913099 + 1.30404i 0.393159 + 4.49382i 1.86939 − 5.13610i 10.1870 − 4.60717i −5.50113 + 4.61600i 7.15577 − 26.7057i 20.7062 − 5.54821i 6.54994 − 1.15493i 15.3096 + 9.07739i
2.18 0.961404 + 1.37303i −0.797037 − 9.11018i 1.77525 − 4.87747i −11.1762 + 0.303590i 11.7422 − 9.85292i −3.48050 + 12.9894i 21.3560 − 5.72232i −55.7702 + 9.83380i −11.1617 − 15.0534i
2.19 1.01359 + 1.44756i 0.774605 + 8.85377i 1.66810 − 4.58306i 9.73411 + 5.49973i −12.0313 + 10.0954i −4.72680 + 17.6406i 21.9805 − 5.88966i −51.1995 + 9.02785i 1.90524 + 19.6652i
2.20 1.07308 + 1.53251i −0.00470693 − 0.0538005i 1.53906 − 4.22853i −11.1517 − 0.799155i 0.0773991 − 0.0649456i 5.96461 − 22.2602i 22.5887 − 6.05261i 26.5869 − 4.68799i −10.7420 − 17.9478i
See next 80 embeddings (of 336 total)
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 2.28
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
19.f odd 18 1 inner
95.r even 36 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 95.4.r.a ✓ 336
5.c odd 4 1 inner 95.4.r.a ✓ 336
19.f odd 18 1 inner 95.4.r.a ✓ 336
95.r even 36 1 inner 95.4.r.a ✓ 336
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.4.r.a ✓ 336 1.a even 1 1 trivial
95.4.r.a ✓ 336 5.c odd 4 1 inner
95.4.r.a ✓ 336 19.f odd 18 1 inner
95.4.r.a ✓ 336 95.r even 36 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(95, [\chi])\).