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Properties

Label 833.2.k.b
Level $833$
Weight $2$
Character orbit 833.k
Analytic conductor $6.652$
Analytic rank $0$
Dimension $216$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [833,2,Mod(120,833)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(833, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([8, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("833.120");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 833.k (of order \(7\), degree \(6\), 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: \(216\)
Relative dimension: \(36\) over \(\Q(\zeta_{7})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 216 q + 2 q^{2} - 2 q^{3} - 34 q^{4} - 2 q^{5} + 8 q^{6} - 4 q^{7} + 12 q^{8} - 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 216 q + 2 q^{2} - 2 q^{3} - 34 q^{4} - 2 q^{5} + 8 q^{6} - 4 q^{7} + 12 q^{8} - 24 q^{9} - 47 q^{10} - 6 q^{12} - 10 q^{13} + q^{14} - 8 q^{15} - 30 q^{16} + 36 q^{17} - 60 q^{18} - 38 q^{19} - 12 q^{20} - 2 q^{21} + 42 q^{22} + 14 q^{23} + 16 q^{24} - 28 q^{25} + 18 q^{26} - 8 q^{27} - 3 q^{28} + 46 q^{29} - 52 q^{30} + 26 q^{31} - 16 q^{32} + 2 q^{33} - 2 q^{34} + 12 q^{35} + 40 q^{36} + 47 q^{37} + 18 q^{38} + 64 q^{39} + 20 q^{40} - 35 q^{41} - 99 q^{42} - 26 q^{43} - 17 q^{44} - 18 q^{45} + 30 q^{46} + 24 q^{47} + 58 q^{48} - 102 q^{49} + 74 q^{50} + 2 q^{51} + 64 q^{52} + 74 q^{53} + 4 q^{54} + 67 q^{55} + 121 q^{56} - 12 q^{57} + 96 q^{58} - 36 q^{59} - 16 q^{60} + 52 q^{61} - 36 q^{62} + 71 q^{63} - 100 q^{64} - 12 q^{65} + 188 q^{66} - 202 q^{67} - 204 q^{68} + 6 q^{69} + 86 q^{70} + 16 q^{71} - 37 q^{72} - 11 q^{73} + 4 q^{74} + 4 q^{75} + 71 q^{76} - 23 q^{77} + 104 q^{78} - 212 q^{79} + 120 q^{80} - 126 q^{81} + 24 q^{82} - 10 q^{83} + 71 q^{84} + 2 q^{85} - 35 q^{86} + 52 q^{87} + 59 q^{88} + 63 q^{89} - 223 q^{90} + 27 q^{91} - 125 q^{92} - 14 q^{93} + q^{94} + 36 q^{95} + 68 q^{96} + 82 q^{97} - 41 q^{98} - 124 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
120.1 −2.38306 + 1.14762i 0.321970 − 1.41064i 3.11496 − 3.90604i −0.249964 + 1.09516i 0.851611 + 3.73115i −1.24419 + 2.33495i −1.76336 + 7.72577i 0.816655 + 0.393280i −0.661154 − 2.89671i
120.2 −2.26847 + 1.09244i 0.244278 − 1.07025i 2.70556 − 3.39267i −0.259044 + 1.13494i 0.615047 + 2.69470i −1.86968 − 1.87198i −1.31068 + 5.74245i 1.61714 + 0.778772i −0.652223 − 2.85758i
120.3 −2.25452 + 1.08572i −0.545735 + 2.39102i 2.65709 − 3.33189i 0.111111 − 0.486810i −1.36561 − 5.98312i −2.51792 + 0.812441i −1.25933 + 5.51748i −2.71625 − 1.30808i 0.278037 + 1.21816i
120.4 −2.09038 + 1.00668i −0.0875490 + 0.383577i 2.10933 − 2.64501i −0.152364 + 0.667550i −0.203127 − 0.889957i 2.64436 + 0.0857961i −0.714070 + 3.12855i 2.56344 + 1.23449i −0.353507 − 1.54882i
120.5 −2.07655 + 1.00002i −0.415957 + 1.82243i 2.06506 − 2.58951i 0.774374 − 3.39275i −0.958697 − 4.20033i −0.141213 − 2.64198i −0.672935 + 2.94832i −0.445309 − 0.214449i 1.78478 + 7.81962i
120.6 −1.88135 + 0.906012i −0.217273 + 0.951937i 1.47165 − 1.84539i −0.972047 + 4.25882i −0.453698 − 1.98778i 0.563641 − 2.58502i −0.167436 + 0.733583i 1.84393 + 0.887990i −2.02977 − 8.89302i
120.7 −1.60960 + 0.775144i 0.717933 − 3.14547i 0.742996 − 0.931687i −0.340150 + 1.49029i 1.28260 + 5.61946i −2.64529 + 0.0492196i 0.321342 − 1.40789i −6.67564 − 3.21482i −0.607686 − 2.66245i
120.8 −1.45494 + 0.700664i 0.0241623 − 0.105862i 0.378950 − 0.475188i 0.781174 − 3.42255i 0.0390189 + 0.170953i 1.40005 + 2.24496i 0.500279 − 2.19187i 2.69228 + 1.29654i 1.26149 + 5.52695i
120.9 −1.32939 + 0.640201i 0.459997 − 2.01538i 0.110442 − 0.138490i 0.531491 − 2.32861i 0.678731 + 2.97371i 0.593220 − 2.57839i 0.598505 − 2.62222i −1.14724 − 0.552483i 0.784221 + 3.43590i
120.10 −1.23630 + 0.595372i −0.561003 + 2.45791i −0.0730014 + 0.0915408i 0.485189 − 2.12575i −0.769805 − 3.37273i 2.47983 − 0.922190i 0.646435 − 2.83221i −3.02371 − 1.45614i 0.665774 + 2.91694i
120.11 −1.06544 + 0.513087i −0.698080 + 3.05849i −0.375084 + 0.470340i −0.726388 + 3.18251i −0.825511 − 3.61680i 0.627397 + 2.57029i 0.684584 − 2.99936i −6.16413 − 2.96849i −0.858986 − 3.76346i
120.12 −1.04610 + 0.503775i −0.146414 + 0.641480i −0.406445 + 0.509666i −0.275494 + 1.20702i −0.169998 − 0.744811i −0.954523 + 2.46757i 0.685155 − 3.00186i 2.31285 + 1.11381i −0.319871 − 1.40145i
120.13 −0.946244 + 0.455687i −0.0874595 + 0.383185i −0.559252 + 0.701280i −0.111091 + 0.486719i −0.0918545 − 0.402441i −2.48685 − 0.903088i 0.677031 − 2.96627i 2.56372 + 1.23462i −0.116673 − 0.511178i
120.14 −0.886712 + 0.427018i 0.164660 − 0.721421i −0.643065 + 0.806378i −0.684768 + 3.00016i 0.162054 + 0.710006i 2.61979 + 0.369765i 0.663875 − 2.90863i 2.20957 + 1.06407i −0.673933 − 2.95269i
120.15 −0.646270 + 0.311227i 0.510237 − 2.23550i −0.926177 + 1.16139i 0.873385 − 3.82655i 0.365996 + 1.60353i −2.50054 + 0.864467i 0.556336 − 2.43747i −2.03419 − 0.979616i 0.626484 + 2.74481i
120.16 −0.282460 + 0.136026i 0.629195 − 2.75668i −1.18570 + 1.48682i −0.0600956 + 0.263296i 0.197257 + 0.864240i 0.591145 + 2.57887i 0.272191 − 1.19255i −4.50050 − 2.16733i −0.0188404 − 0.0825453i
120.17 −0.148276 + 0.0714062i −0.528129 + 2.31388i −1.23009 + 1.54249i −0.487401 + 2.13544i −0.0869166 − 0.380806i 0.204776 − 2.63781i 0.145493 − 0.637447i −2.37224 − 1.14241i −0.0802137 − 0.351439i
120.18 −0.00700452 + 0.00337320i 0.206166 − 0.903274i −1.24694 + 1.56362i 0.403062 − 1.76593i 0.00160283 + 0.00702244i 0.307923 − 2.62777i 0.00691979 − 0.0303176i 1.92951 + 0.929202i 0.00313358 + 0.0137291i
120.19 0.141687 − 0.0682328i 0.565487 − 2.47756i −1.23156 + 1.54433i −0.562100 + 2.46272i −0.0889289 − 0.389623i 2.59796 − 0.500606i −0.139110 + 0.609479i −3.11563 − 1.50041i 0.0883962 + 0.387289i
120.20 0.359394 − 0.173075i −0.755636 + 3.31066i −1.14777 + 1.43926i 0.681301 − 2.98498i 0.301421 + 1.32061i −1.43552 − 2.22245i −0.340928 + 1.49370i −7.68657 − 3.70166i −0.271769 − 1.19070i
See next 80 embeddings (of 216 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 120.36
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
49.e even 7 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 833.2.k.b ✓ 216
49.e even 7 1 inner 833.2.k.b ✓ 216
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
833.2.k.b ✓ 216 1.a even 1 1 trivial
833.2.k.b ✓ 216 49.e even 7 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{216} - 2 T_{2}^{215} + 55 T_{2}^{214} - 114 T_{2}^{213} + 1655 T_{2}^{212} - 3498 T_{2}^{211} + \cdots + 2801462495049 \) acting on \(S_{2}^{\mathrm{new}}(833, [\chi])\). Copy content Toggle raw display