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Properties

Label 833.2.bf.a
Level $833$
Weight $2$
Character orbit 833.bf
Analytic conductor $6.652$
Analytic rank $0$
Dimension $1968$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [833,2,Mod(8,833)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(833, base_ring=CyclotomicField(56))
 
chi = DirichletCharacter(H, H._module([48, 35]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("833.8");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 833.bf (of order \(56\), degree \(24\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.65153848837\)
Analytic rank: \(0\)
Dimension: \(1968\)
Relative dimension: \(82\) over \(\Q(\zeta_{56})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{56}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1968 q - 20 q^{2} - 20 q^{3} - 28 q^{5} - 20 q^{6} - 24 q^{7} - 36 q^{8} - 20 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 1968 q - 20 q^{2} - 20 q^{3} - 28 q^{5} - 20 q^{6} - 24 q^{7} - 36 q^{8} - 20 q^{9} - 20 q^{10} - 40 q^{11} - 44 q^{12} - 32 q^{14} + 4 q^{15} + 264 q^{16} - 36 q^{17} - 64 q^{18} - 48 q^{19} - 52 q^{20} - 52 q^{22} + 40 q^{23} - 92 q^{24} - 12 q^{25} - 4 q^{26} - 68 q^{27} - 200 q^{28} - 20 q^{29} - 48 q^{31} - 76 q^{32} - 40 q^{33} - 20 q^{34} - 32 q^{35} - 92 q^{36} + 12 q^{37} - 44 q^{39} - 212 q^{40} + 44 q^{41} + 92 q^{42} - 20 q^{43} - 132 q^{44} - 44 q^{45} - 20 q^{46} + 24 q^{48} - 148 q^{49} - 128 q^{50} - 100 q^{51} - 152 q^{52} - 20 q^{53} - 88 q^{54} - 8 q^{56} - 20 q^{57} + 60 q^{58} + 20 q^{59} - 108 q^{60} + 20 q^{61} + 84 q^{62} - 60 q^{65} - 4 q^{66} - 112 q^{67} - 32 q^{68} - 344 q^{69} - 36 q^{70} + 156 q^{71} + 20 q^{73} - 20 q^{74} - 316 q^{75} + 100 q^{76} - 52 q^{77} - 276 q^{78} - 80 q^{79} - 112 q^{80} - 216 q^{82} - 8 q^{83} - 136 q^{84} - 12 q^{85} - 104 q^{86} - 20 q^{87} + 168 q^{88} + 60 q^{90} - 36 q^{91} + 28 q^{92} + 120 q^{93} - 212 q^{94} + 132 q^{95} + 236 q^{96} - 96 q^{97} + 400 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
8.1 −2.77909 − 0.313128i 0.0180979 + 0.322262i 5.67543 + 1.29538i −0.420472 + 0.0236132i 0.0506138 − 0.901263i −1.81132 − 1.92850i −10.0874 − 3.52975i 2.87761 − 0.324229i 1.17592 + 0.0660384i
8.2 −2.72014 − 0.306486i −0.172868 − 3.07820i 5.35536 + 1.22233i 2.13107 − 0.119678i −0.473201 + 8.42612i −1.89435 − 1.84701i −9.02520 − 3.15806i −6.46433 + 0.728355i −5.83347 − 0.327601i
8.3 −2.62578 − 0.295854i −0.0828161 − 1.47468i 4.85733 + 1.10865i −1.70981 + 0.0960209i −0.218833 + 3.89668i 0.707527 + 2.54939i −7.43804 − 2.60268i 0.813320 − 0.0916391i 4.51799 + 0.253725i
8.4 −2.58680 − 0.291462i 0.109559 + 1.95088i 4.65673 + 1.06287i −3.48241 + 0.195568i 0.285200 − 5.07847i 2.62240 − 0.350733i −6.82206 − 2.38714i −0.812788 + 0.0915792i 9.06531 + 0.509097i
8.5 −2.45787 − 0.276935i −0.143327 − 2.55218i 4.01456 + 0.916297i −3.22707 + 0.181228i −0.354509 + 6.31261i 2.09392 − 1.61726i −4.94426 − 1.73007i −3.51195 + 0.395702i 7.98190 + 0.448254i
8.6 −2.43989 − 0.274910i −0.0158559 − 0.282341i 3.92764 + 0.896458i 1.38582 − 0.0778261i −0.0389315 + 0.693240i 0.231078 + 2.63564i −4.70148 − 1.64512i 2.90167 − 0.326940i −3.40265 − 0.191089i
8.7 −2.43216 − 0.274039i −0.0779283 − 1.38764i 3.89047 + 0.887975i 3.05073 − 0.171325i −0.190734 + 3.39633i 2.59061 − 0.537330i −4.59852 − 1.60909i 1.06166 − 0.119620i −7.46683 − 0.419328i
8.8 −2.38157 − 0.268338i 0.143293 + 2.55157i 3.64999 + 0.833087i 3.47541 − 0.195175i 0.343421 − 6.11518i −0.201275 − 2.63808i −3.94486 − 1.38037i −3.50885 + 0.395352i −8.32928 − 0.467763i
8.9 −2.37780 − 0.267913i 0.0609270 + 1.08491i 3.63228 + 0.829045i 3.87474 − 0.217601i 0.145789 − 2.59601i −2.15077 + 1.54085i −3.89759 − 1.36383i 1.80783 − 0.203693i −9.27165 − 0.520685i
8.10 −2.28812 − 0.257809i 0.187152 + 3.33256i 3.21917 + 0.734753i −2.18450 + 0.122679i 0.430937 − 7.67354i −2.28974 − 1.32555i −2.82964 − 0.990134i −8.08978 + 0.911499i 5.03002 + 0.282480i
8.11 −2.26894 − 0.255648i 0.167635 + 2.98501i 3.13288 + 0.715060i 0.439891 − 0.0247037i 0.382760 − 6.81568i 0.982675 + 2.45649i −2.61519 − 0.915095i −5.90107 + 0.664890i −1.00440 − 0.0564060i
8.12 −2.25182 − 0.253719i 0.0665970 + 1.18587i 3.05645 + 0.697615i 0.568370 − 0.0319190i 0.150913 − 2.68726i 1.72262 − 2.00813i −2.42777 − 0.849514i 1.57928 − 0.177943i −1.28796 − 0.0723305i
8.13 −2.23898 − 0.252272i 0.0458532 + 0.816491i 2.99951 + 0.684620i −2.45731 + 0.137999i 0.103314 − 1.83967i −2.53885 + 0.744469i −2.28972 − 0.801208i 2.31658 − 0.261016i 5.53667 + 0.310932i
8.14 −2.14621 − 0.241820i −0.104890 − 1.86773i 2.59790 + 0.592955i −3.69409 + 0.207456i −0.226540 + 4.03392i −2.56480 + 0.649470i −1.35508 − 0.474164i −0.496295 + 0.0559190i 7.97847 + 0.448061i
8.15 −1.95935 − 0.220766i −0.138259 − 2.46194i 1.84047 + 0.420076i −0.677666 + 0.0380569i −0.272613 + 4.85433i 0.506690 − 2.59678i 0.208808 + 0.0730652i −3.06089 + 0.344879i 1.33619 + 0.0750388i
8.16 −1.89016 − 0.212970i 0.0447061 + 0.796066i 1.57749 + 0.360051i −0.824415 + 0.0462982i 0.0850363 − 1.51421i 2.64158 − 0.148523i 0.685738 + 0.239950i 2.34941 − 0.264715i 1.56814 + 0.0880646i
8.17 −1.84717 − 0.208126i −0.0967216 − 1.72229i 1.41887 + 0.323848i 1.68133 − 0.0944215i −0.179792 + 3.20149i −2.63680 − 0.217494i 0.955596 + 0.334377i 0.0242177 − 0.00272867i −3.12536 − 0.175516i
8.18 −1.78704 − 0.201351i 0.0679188 + 1.20941i 1.20311 + 0.274602i −1.25260 + 0.0703445i 0.122142 − 2.17493i −0.122384 + 2.64292i 1.30015 + 0.454942i 1.52308 − 0.171610i 2.25261 + 0.126504i
8.19 −1.78164 − 0.200742i −0.163778 − 2.91635i 1.18407 + 0.270257i 3.94021 − 0.221277i −0.293640 + 5.22874i 1.34417 + 2.27886i 1.32926 + 0.465127i −5.49711 + 0.619376i −7.06443 − 0.396730i
8.20 −1.61679 − 0.182168i −0.110036 − 1.95938i 0.630958 + 0.144012i −0.679247 + 0.0381457i −0.179031 + 3.18794i 2.60058 + 0.486829i 2.07754 + 0.726962i −0.845912 + 0.0953114i 1.10515 + 0.0620637i
See next 80 embeddings (of 1968 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 8.82
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
17.d even 8 1 inner
49.e even 7 1 inner
833.bf even 56 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 833.2.bf.a ✓ 1968
17.d even 8 1 inner 833.2.bf.a ✓ 1968
49.e even 7 1 inner 833.2.bf.a ✓ 1968
833.bf even 56 1 inner 833.2.bf.a ✓ 1968
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
833.2.bf.a ✓ 1968 1.a even 1 1 trivial
833.2.bf.a ✓ 1968 17.d even 8 1 inner
833.2.bf.a ✓ 1968 49.e even 7 1 inner
833.2.bf.a ✓ 1968 833.bf even 56 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(833, [\chi])\).