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Properties

Label 833.2.bc.d
Level $833$
Weight $2$
Character orbit 833.bc
Analytic conductor $6.652$
Analytic rank $0$
Dimension $144$
Inner twists $4$

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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] = [833,2,Mod(31,833)] 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("833.31"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(833, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([8, 27])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 833.bc (of order \(48\), degree \(16\), not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [144,0,8,0,8,-16,0,0,-24,0,-8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.65153848837\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(9\) over \(\Q(\zeta_{48})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{48}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 144 q + 8 q^{3} + 8 q^{5} - 16 q^{6} - 24 q^{9} - 8 q^{11} + 64 q^{13} + 40 q^{18} + 24 q^{19} + 48 q^{22} - 8 q^{23} - 24 q^{24} - 8 q^{25} - 16 q^{27} + 80 q^{31} + 40 q^{32} - 80 q^{33} + 240 q^{36}+ \cdots + 80 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
31.1 −2.00606 − 1.53930i −0.614944 + 0.701209i 1.13718 + 4.24400i −0.794586 + 1.61126i 2.31298 − 0.460081i 0 2.31626 − 5.59195i 0.278040 + 2.11193i 4.07420 − 2.00917i
31.2 −1.87782 − 1.44090i 2.02420 − 2.30815i 0.932371 + 3.47966i 0.945105 − 1.91648i −7.12690 + 1.41763i 0 1.45144 − 3.50409i −0.838624 − 6.36998i −4.53620 + 2.23701i
31.3 −1.17548 − 0.901974i −1.45584 + 1.66007i 0.0505477 + 0.188647i 1.17787 − 2.38849i 3.20864 − 0.638239i 0 −1.02327 + 2.47040i −0.244775 − 1.85925i −3.53891 + 1.74520i
31.4 −0.683820 − 0.524714i 0.998622 − 1.13871i −0.325353 − 1.21423i −1.29515 + 2.62630i −1.28037 + 0.254682i 0 −1.07434 + 2.59368i 0.0921635 + 0.700051i 2.26370 − 1.11633i
31.5 0.305048 + 0.234071i −0.951018 + 1.08443i −0.479373 − 1.78905i −0.668546 + 1.35568i −0.543939 + 0.108196i 0 0.566820 − 1.36842i 0.120030 + 0.911715i −0.521264 + 0.257059i
31.6 0.846061 + 0.649206i 1.90514 − 2.17239i −0.223286 − 0.833316i 0.302561 − 0.613533i 3.02219 − 0.601151i 0 1.16830 − 2.82051i −0.698161 − 5.30306i 0.654294 − 0.322662i
31.7 1.30884 + 1.00431i −0.323209 + 0.368549i 0.186787 + 0.697097i 1.14184 − 2.31542i −0.793165 + 0.157770i 0 0.807041 − 1.94837i 0.360214 + 2.73610i 3.81987 − 1.88375i
31.8 1.87626 + 1.43970i −2.17524 + 2.48039i 0.929961 + 3.47066i −0.831485 + 1.68608i −7.65233 + 1.52214i 0 −1.44181 + 3.48083i −1.02907 − 7.81654i −3.98754 + 1.96644i
31.9 2.20032 + 1.68837i 1.15302 − 1.31477i 1.47319 + 5.49804i −0.123911 + 0.251267i 4.75684 − 0.946194i 0 −3.91849 + 9.46008i −0.00758215 − 0.0575922i −0.696875 + 0.343660i
80.1 −1.62368 + 2.11602i −1.24399 + 0.0815353i −1.32356 − 4.93960i −0.496521 + 0.168546i 1.84730 − 2.76469i 0 7.67299 + 3.17826i −1.43348 + 0.188721i 0.449543 − 1.32431i
80.2 −1.08860 + 1.41869i 0.543906 − 0.0356495i −0.309994 − 1.15691i 2.53857 − 0.861728i −0.541520 + 0.810442i 0 −1.32544 − 0.549014i −2.67977 + 0.352799i −1.54096 + 4.53951i
80.3 −0.956451 + 1.24647i 2.12823 − 0.139492i −0.121254 − 0.452528i −1.16615 + 0.395855i −1.86168 + 2.78620i 0 −2.22306 − 0.920820i 1.53557 − 0.202162i 0.621946 − 1.83219i
80.4 −0.401850 + 0.523701i −1.70229 + 0.111574i 0.404859 + 1.51095i −4.12154 + 1.39907i 0.625632 − 0.936325i 0 −2.17370 − 0.900378i −0.0889981 + 0.0117168i 0.923543 − 2.72067i
80.5 0.0366505 − 0.0477639i −1.14645 + 0.0751426i 0.516700 + 1.92835i 2.21610 − 0.752264i −0.0384290 + 0.0575131i 0 0.222287 + 0.0920744i −1.66562 + 0.219283i 0.0452901 − 0.133420i
80.6 0.671839 − 0.875557i 2.47510 − 0.162227i 0.202405 + 0.755385i −1.79717 + 0.610057i 1.52083 − 2.27608i 0 2.83658 + 1.17495i 3.12548 − 0.411477i −0.673269 + 1.98339i
80.7 1.06917 − 1.39336i −2.43686 + 0.159720i −0.280710 − 1.04763i −0.476721 + 0.161825i −2.38286 + 3.56621i 0 1.48536 + 0.615258i 2.93846 − 0.386855i −0.284213 + 0.837263i
80.8 1.22189 − 1.59240i 1.47857 − 0.0969109i −0.525080 − 1.95963i 3.60921 − 1.22516i 1.65234 − 2.47290i 0 −0.0533216 − 0.0220865i −0.797544 + 0.104999i 2.45911 − 7.24431i
80.9 1.67979 − 2.18914i 0.623197 − 0.0408465i −1.45302 − 5.42276i −3.08567 + 1.04744i 0.957422 − 1.43288i 0 −9.21334 − 3.81629i −2.58763 + 0.340668i −2.89027 + 8.51446i
129.1 −2.73575 + 0.360168i −0.276225 − 0.560128i 5.42276 − 1.45302i 2.44995 − 2.14855i 0.957422 + 1.43288i 0 −9.21334 + 3.81629i 1.58884 − 2.07062i −5.92861 + 6.76028i
129.2 −1.99000 + 0.261989i −0.655360 − 1.32894i 1.95963 − 0.525080i −2.86562 + 2.51308i 1.65234 + 2.47290i 0 −0.0533216 + 0.0220865i 0.489703 − 0.638194i 5.04420 − 5.75181i
See next 80 embeddings (of 144 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 31.9
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.c even 3 1 inner
119.p even 16 1 inner
119.s even 48 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 833.2.bc.d 144
7.b odd 2 1 833.2.bc.a 144
7.c even 3 1 833.2.t.a ✓ 72
7.c even 3 1 inner 833.2.bc.d 144
7.d odd 6 1 833.2.t.d yes 72
7.d odd 6 1 833.2.bc.a 144
17.e odd 16 1 833.2.bc.a 144
119.p even 16 1 inner 833.2.bc.d 144
119.s even 48 1 833.2.t.a ✓ 72
119.s even 48 1 inner 833.2.bc.d 144
119.t odd 48 1 833.2.t.d yes 72
119.t odd 48 1 833.2.bc.a 144
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
833.2.t.a ✓ 72 7.c even 3 1
833.2.t.a ✓ 72 119.s even 48 1
833.2.t.d yes 72 7.d odd 6 1
833.2.t.d yes 72 119.t odd 48 1
833.2.bc.a 144 7.b odd 2 1
833.2.bc.a 144 7.d odd 6 1
833.2.bc.a 144 17.e odd 16 1
833.2.bc.a 144 119.t odd 48 1
833.2.bc.d 144 1.a even 1 1 trivial
833.2.bc.d 144 7.c even 3 1 inner
833.2.bc.d 144 119.p even 16 1 inner
833.2.bc.d 144 119.s even 48 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(833, [\chi])\):

\( T_{2}^{144} - 8 T_{2}^{139} + 72 T_{2}^{137} - 5079 T_{2}^{136} - 1152 T_{2}^{135} + 496 T_{2}^{134} + \cdots + 260144641 \) Copy content Toggle raw display
\( T_{3}^{144} - 8 T_{3}^{143} + 44 T_{3}^{142} - 176 T_{3}^{141} + 624 T_{3}^{140} - 1776 T_{3}^{139} + \cdots + 12\!\cdots\!64 \) Copy content Toggle raw display