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Properties

Label 833.2.u.a
Level $833$
Weight $2$
Character orbit 833.u
Analytic conductor $6.652$
Analytic rank $0$
Dimension $420$
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(86,833)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(833, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([32, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("833.86");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 833.u (of order \(21\), degree \(12\), 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: \(420\)
Relative dimension: \(35\) over \(\Q(\zeta_{21})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{21}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 420 q - 2 q^{2} + q^{3} + 30 q^{4} + 2 q^{5} - 14 q^{6} + 6 q^{8} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 420 q - 2 q^{2} + q^{3} + 30 q^{4} + 2 q^{5} - 14 q^{6} + 6 q^{8} + 14 q^{9} - 94 q^{10} - 6 q^{11} + 2 q^{12} + 8 q^{13} - 7 q^{14} + 44 q^{15} + 20 q^{16} - 35 q^{17} + 60 q^{18} - 15 q^{19} - 24 q^{20} - 14 q^{21} - 14 q^{23} + 17 q^{24} + 21 q^{25} - 12 q^{26} - 8 q^{27} - 7 q^{28} - 28 q^{29} + 46 q^{30} - 34 q^{31} - 218 q^{32} + q^{33} - 4 q^{34} - 21 q^{35} - 98 q^{36} - 42 q^{37} + 9 q^{38} + q^{39} + 82 q^{40} + 11 q^{41} + 84 q^{42} + 84 q^{43} + 113 q^{44} + 15 q^{45} + 60 q^{46} + 14 q^{48} + 98 q^{49} - 254 q^{50} - q^{51} + 73 q^{52} - 23 q^{53} + 116 q^{54} - 79 q^{55} + 14 q^{56} + 34 q^{57} - 69 q^{58} - 93 q^{59} + 124 q^{60} - 11 q^{61} - 42 q^{62} - 56 q^{63} + 78 q^{64} - 18 q^{65} - 152 q^{66} + 194 q^{67} + 180 q^{68} - 72 q^{69} - 77 q^{70} + 38 q^{71} - 473 q^{72} - 28 q^{74} + 16 q^{75} - 139 q^{76} - 112 q^{77} - 44 q^{78} + 207 q^{79} - 48 q^{80} - 475 q^{81} - 42 q^{82} + 22 q^{83} + 147 q^{84} + 4 q^{85} - 187 q^{86} + 113 q^{87} - 23 q^{88} + 39 q^{89} + 535 q^{90} + 70 q^{91} + 188 q^{92} + 33 q^{93} + 155 q^{94} - 18 q^{95} - 80 q^{96} - 54 q^{97} + 182 q^{98} - 236 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
86.1 −2.20333 + 1.50220i −0.0185531 + 0.0172147i 1.86736 − 4.75796i −3.45538 − 1.06584i 0.0150185 − 0.0658002i 2.11835 − 1.58512i 1.84622 + 8.08883i −0.224142 + 2.99097i 9.21446 − 2.84229i
86.2 −2.09882 + 1.43095i 0.348165 − 0.323050i 1.62674 − 4.14487i 2.49521 + 0.769671i −0.268467 + 1.17623i −1.84271 − 1.89853i 1.38637 + 6.07409i −0.207333 + 2.76666i −6.33836 + 1.95513i
86.3 −1.95970 + 1.33610i −1.38206 + 1.28237i 1.32458 − 3.37497i 2.44912 + 0.755453i 0.995057 − 4.35963i −2.35038 + 1.21480i 0.857960 + 3.75897i 0.0414422 − 0.553007i −5.80890 + 1.79181i
86.4 −1.93930 + 1.32219i 1.63442 − 1.51652i 1.28201 − 3.26651i 1.42643 + 0.439995i −1.16450 + 5.10201i 2.14425 − 1.54990i 0.788177 + 3.45323i 0.147305 − 1.96565i −3.34803 + 1.03273i
86.5 −1.83369 + 1.25019i 2.49179 − 2.31205i 1.06877 − 2.72318i 4.01758 + 1.23926i −1.67868 + 7.35480i −1.47378 + 2.19726i 0.457009 + 2.00229i 0.639285 − 8.53067i −8.91632 + 2.75032i
86.6 −1.67230 + 1.14015i 0.956655 − 0.887646i 0.765945 − 1.95160i −0.518012 − 0.159786i −0.587759 + 2.57514i 1.54239 + 2.14966i 0.0434706 + 0.190457i −0.0969171 + 1.29327i 1.04845 − 0.323404i
86.7 −1.52951 + 1.04280i −1.88511 + 1.74912i 0.521275 − 1.32819i −1.36598 − 0.421348i 1.05930 − 4.64108i −1.07623 − 2.41697i −0.236108 − 1.03445i 0.270003 − 3.60295i 2.52865 − 0.779984i
86.8 −1.44071 + 0.982258i −0.0913299 + 0.0847418i 0.380125 − 0.968543i −1.75134 − 0.540218i 0.0483414 − 0.211798i 1.16062 + 2.37760i −0.372307 − 1.63118i −0.223030 + 2.97613i 3.05381 − 0.941975i
86.9 −1.34028 + 0.913788i −2.43361 + 2.25806i 0.230661 − 0.587715i 3.10244 + 0.956977i 1.19833 − 5.25023i 2.00053 + 1.73144i −0.494027 − 2.16447i 0.599429 − 7.99883i −5.03262 + 1.55236i
86.10 −1.22045 + 0.832092i −0.761855 + 0.706898i 0.0664503 − 0.169313i 3.04752 + 0.940037i 0.341605 − 1.49667i 0.494246 − 2.59918i −0.597596 − 2.61824i −0.143472 + 1.91450i −4.50156 + 1.38855i
86.11 −1.15014 + 0.784149i 1.41712 − 1.31489i −0.0227603 + 0.0579923i −1.33798 − 0.412713i −0.598804 + 2.62353i −2.30613 + 1.29682i −0.638801 − 2.79877i 0.0550879 − 0.735097i 1.86249 − 0.574502i
86.12 −0.905216 + 0.617166i −0.706183 + 0.655242i −0.292159 + 0.744410i −0.397932 − 0.122746i 0.234855 − 1.02897i −2.64295 − 0.121791i −0.682539 − 2.99040i −0.154838 + 2.06617i 0.435969 − 0.134479i
86.13 −0.823398 + 0.561383i 1.18142 − 1.09620i −0.367849 + 0.937263i −3.49600 − 1.07837i −0.357391 + 1.56583i −0.388118 − 2.61713i −0.666790 − 2.92140i −0.0300870 + 0.401483i 3.48398 − 1.07467i
86.14 −0.762894 + 0.520132i −2.37281 + 2.20164i −0.419212 + 1.06814i −2.38943 − 0.737042i 0.665055 − 2.91380i −1.09233 + 2.40973i −0.646679 − 2.83329i 0.558791 − 7.45655i 2.20624 − 0.680535i
86.15 −0.715434 + 0.487775i −0.171182 + 0.158833i −0.456760 + 1.16381i −0.792721 − 0.244522i 0.0449943 − 0.197133i 2.51161 − 0.831769i −0.626252 − 2.74379i −0.220115 + 2.93723i 0.686411 − 0.211730i
86.16 −0.364215 + 0.248317i 2.36050 − 2.19022i −0.659691 + 1.68087i −0.349842 − 0.107912i −0.315858 + 1.38386i 2.40877 − 1.09444i −0.373298 − 1.63553i 0.550688 − 7.34842i 0.154214 − 0.0475688i
86.17 −0.297793 + 0.203032i 1.17504 − 1.09027i −0.683223 + 1.74082i 2.41895 + 0.746148i −0.128557 + 0.563246i −0.150614 + 2.64146i −0.310386 − 1.35989i −0.0321785 + 0.429392i −0.871839 + 0.268927i
86.18 −0.0281829 + 0.0192148i −0.764287 + 0.709154i −0.730257 + 1.86066i −3.37178 − 1.04006i 0.00791358 − 0.0346716i −2.37314 + 1.16971i −0.0303518 − 0.132980i −0.142956 + 1.90762i 0.115011 − 0.0354762i
86.19 0.0117815 − 0.00803250i −0.777566 + 0.721476i −0.730608 + 1.86156i 2.93713 + 0.905984i −0.00336565 + 0.0147459i 1.25706 + 2.32804i 0.0126912 + 0.0556040i −0.140109 + 1.86962i 0.0418811 − 0.0129186i
86.20 0.374607 − 0.255403i −0.397966 + 0.369259i −0.655582 + 1.67040i 1.51775 + 0.468164i −0.0547713 + 0.239969i −0.193919 − 2.63864i 0.382815 + 1.67722i −0.202165 + 2.69771i 0.688130 − 0.212260i
See next 80 embeddings (of 420 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 86.35
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
49.g even 21 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 833.2.u.a ✓ 420
49.g even 21 1 inner 833.2.u.a ✓ 420
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
833.2.u.a ✓ 420 1.a even 1 1 trivial
833.2.u.a ✓ 420 49.g even 21 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{420} + 2 T_{2}^{419} - 48 T_{2}^{418} - 106 T_{2}^{417} + 1016 T_{2}^{416} + \cdots + 86\!\cdots\!01 \) acting on \(S_{2}^{\mathrm{new}}(833, [\chi])\). Copy content Toggle raw display