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Properties

Label 95.2.r.a
Level $95$
Weight $2$
Character orbit 95.r
Analytic conductor $0.759$
Analytic rank $0$
Dimension $96$
Inner twists $4$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [95,2,Mod(2,95)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(95, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([9, 2])) N = Newforms(chi, 2, names="a")
 
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, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
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: \(0.758578819202\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(8\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 96 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 12 q^{6} - 18 q^{8} - 12 q^{10} - 12 q^{11} - 18 q^{12} - 12 q^{13} + 6 q^{15} + 12 q^{16} - 30 q^{17} - 84 q^{20} + 24 q^{21} - 24 q^{22} + 12 q^{25} - 48 q^{26}+ \cdots - 90 q^{98}+O(q^{100}) \) 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 −1.34445 − 1.92007i 0.165797 + 1.89507i −1.19510 + 3.28350i 0.624382 + 2.14713i 3.41577 − 2.86617i −0.719307 + 2.68449i 3.38309 − 0.906496i −0.609382 + 0.107451i 3.28319 − 4.08556i
2.2 −1.06046 − 1.51450i 0.101890 + 1.16461i −0.485079 + 1.33274i −0.767519 − 2.10022i 1.65575 − 1.38934i 1.17582 − 4.38823i −1.03888 + 0.278366i 1.60848 − 0.283619i −2.36685 + 3.38961i
2.3 −0.983828 − 1.40505i −0.215709 − 2.46557i −0.322212 + 0.885271i 2.19633 + 0.419667i −3.25203 + 2.72877i 0.0743036 − 0.277305i −1.75276 + 0.469650i −3.07806 + 0.542745i −1.57116 − 3.49884i
2.4 −0.425033 − 0.607009i −0.144020 − 1.64615i 0.496232 − 1.36339i −2.21638 − 0.296102i −0.938018 + 0.787091i −0.706367 + 2.63620i −2.47005 + 0.661847i 0.265340 − 0.0467866i 0.762295 + 1.47121i
2.5 0.0545146 + 0.0778549i 0.111718 + 1.27695i 0.680951 − 1.87090i 1.20455 − 1.88389i −0.0933263 + 0.0783101i −0.883627 + 3.29774i 0.366390 − 0.0981738i 1.33631 − 0.235628i 0.212336 − 0.00891912i
2.6 0.259809 + 0.371046i 0.264820 + 3.02691i 0.613866 − 1.68658i −1.63140 + 1.52922i −1.05432 + 0.884679i 0.508516 − 1.89781i 1.66034 − 0.444888i −6.13763 + 1.08223i −0.991264 − 0.208020i
2.7 0.583359 + 0.833123i −0.155202 − 1.77397i 0.330254 − 0.907365i −0.148012 + 2.23116i 1.38740 − 1.16417i 0.267922 − 0.999898i 2.91340 − 0.780644i −0.168464 + 0.0297048i −1.94518 + 1.17826i
2.8 1.31842 + 1.88289i 0.0291608 + 0.333309i −1.12303 + 3.08549i −1.96769 − 1.06216i −0.589140 + 0.494347i 0.282738 − 1.05519i −2.84973 + 0.763583i 2.84418 − 0.501505i −0.594310 − 5.10532i
3.1 −0.230116 − 2.63024i 0.901235 − 1.93270i −4.89558 + 0.863222i 1.62989 + 1.53084i −5.29086 − 1.92571i 1.39789 + 0.374564i 2.03032 + 7.57725i −0.994759 − 1.18551i 3.65140 − 4.63926i
3.2 −0.140400 − 1.60478i 0.303112 − 0.650026i −0.585979 + 0.103324i −1.97659 − 1.04551i −1.08570 − 0.395164i 1.05988 + 0.283994i −0.585783 − 2.18617i 1.59771 + 1.90407i −1.40029 + 3.31878i
3.3 −0.119667 − 1.36780i −0.753423 + 1.61572i 0.113072 − 0.0199376i 2.23461 − 0.0806865i 2.30013 + 0.837180i −0.254507 − 0.0681949i −0.751529 − 2.80474i −0.114542 − 0.136506i −0.377771 − 3.04684i
3.4 0.0260387 + 0.297624i −0.818952 + 1.75625i 1.88171 − 0.331797i −1.72736 + 1.41994i −0.544026 − 0.198009i −0.323332 − 0.0866366i 0.302398 + 1.12856i −0.485360 − 0.578430i −0.467587 − 0.477130i
3.5 0.0741107 + 0.847089i 0.344068 − 0.737855i 1.25755 − 0.221740i 0.654653 − 2.13809i 0.650528 + 0.236773i −3.83889 − 1.02863i 0.721192 + 2.69152i 1.50231 + 1.79039i 1.85967 + 0.396094i
3.6 0.148765 + 1.70039i 1.25242 − 2.68582i −0.899578 + 0.158620i −2.22976 + 0.167893i 4.75325 + 1.73004i 2.71511 + 0.727512i 0.480007 + 1.79141i −3.71671 − 4.42940i −0.617193 − 3.76648i
3.7 0.184204 + 2.10547i −1.05623 + 2.26510i −2.42944 + 0.428375i 0.118240 − 2.23294i −4.96365 − 1.80662i 2.23442 + 0.598711i −0.255410 − 0.953204i −2.08669 − 2.48682i 4.72316 − 0.162367i
3.8 0.215520 + 2.46340i 0.236608 − 0.507407i −4.05227 + 0.714525i 1.40966 + 1.73576i 1.30094 + 0.473503i −2.99058 − 0.801323i −1.35349 − 5.05128i 1.72688 + 2.05802i −3.97207 + 3.84663i
13.1 −2.46340 − 0.215520i −0.507407 + 0.236608i 4.05227 + 0.714525i −1.91831 − 1.14895i 1.30094 − 0.473503i 0.801323 + 2.99058i −5.05128 − 1.35349i −1.72688 + 2.05802i 4.47794 + 3.24376i
13.2 −2.10547 − 0.184204i 2.26510 − 1.05623i 2.42944 + 0.428375i 0.652601 + 2.13872i −4.96365 + 1.80662i −0.598711 − 2.23442i −0.953204 − 0.255410i 2.08669 − 2.48682i −0.980068 − 4.62321i
13.3 −1.70039 − 0.148765i −2.68582 + 1.25242i 0.899578 + 0.158620i 2.03786 − 0.920389i 4.75325 − 1.73004i −0.727512 − 2.71511i 1.79141 + 0.480007i 3.71671 − 4.42940i −3.60208 + 1.26186i
13.4 −0.847089 − 0.0741107i −0.737855 + 0.344068i −1.25755 − 0.221740i 0.116098 + 2.23305i 0.650528 − 0.236773i 1.02863 + 3.83889i 2.69152 + 0.721192i −1.50231 + 1.79039i 0.0671479 − 1.90020i
See all 96 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 2.8
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 95.2.r.a ✓ 96
3.b odd 2 1 855.2.dl.a 96
5.b even 2 1 475.2.bb.b 96
5.c odd 4 1 inner 95.2.r.a ✓ 96
5.c odd 4 1 475.2.bb.b 96
15.e even 4 1 855.2.dl.a 96
19.f odd 18 1 inner 95.2.r.a ✓ 96
57.j even 18 1 855.2.dl.a 96
95.o odd 18 1 475.2.bb.b 96
95.r even 36 1 inner 95.2.r.a ✓ 96
95.r even 36 1 475.2.bb.b 96
285.bj odd 36 1 855.2.dl.a 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
95.2.r.a ✓ 96 1.a even 1 1 trivial
95.2.r.a ✓ 96 5.c odd 4 1 inner
95.2.r.a ✓ 96 19.f odd 18 1 inner
95.2.r.a ✓ 96 95.r even 36 1 inner
475.2.bb.b 96 5.b even 2 1
475.2.bb.b 96 5.c odd 4 1
475.2.bb.b 96 95.o odd 18 1
475.2.bb.b 96 95.r even 36 1
855.2.dl.a 96 3.b odd 2 1
855.2.dl.a 96 15.e even 4 1
855.2.dl.a 96 57.j even 18 1
855.2.dl.a 96 285.bj odd 36 1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(95, [\chi])\).