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Properties

Label 833.2.bn.a
Level $833$
Weight $2$
Character orbit 833.bn
Analytic conductor $6.652$
Analytic rank $0$
Dimension $7872$
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(3,833)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(833, base_ring=CyclotomicField(336))
 
chi = DirichletCharacter(H, H._module([8, 21]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("833.3");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 833.bn (of order \(336\), degree \(96\), 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: \(7872\)
Relative dimension: \(82\) over \(\Q(\zeta_{336})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{336}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 7872 q - 104 q^{2} - 88 q^{3} - 104 q^{4} - 88 q^{5} - 112 q^{6} - 96 q^{7} - 80 q^{8} - 104 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 7872 q - 104 q^{2} - 88 q^{3} - 104 q^{4} - 88 q^{5} - 112 q^{6} - 96 q^{7} - 80 q^{8} - 104 q^{9} - 88 q^{10} - 168 q^{11} - 88 q^{12} - 112 q^{13} - 80 q^{14} - 128 q^{15} - 88 q^{17} - 128 q^{18} - 144 q^{19} - 112 q^{20} - 72 q^{21} - 112 q^{22} - 104 q^{23} - 88 q^{24} - 112 q^{25} - 88 q^{26} - 112 q^{27} + 192 q^{28} - 80 q^{29} - 112 q^{30} - 144 q^{31} - 72 q^{32} - 112 q^{34} - 224 q^{35} - 136 q^{37} - 88 q^{38} - 104 q^{39} - 536 q^{40} - 112 q^{41} - 240 q^{42} - 80 q^{43} - 360 q^{44} - 88 q^{45} - 104 q^{46} - 88 q^{47} + 288 q^{49} - 104 q^{51} - 176 q^{52} - 104 q^{53} - 40 q^{54} - 112 q^{55} - 216 q^{56} - 80 q^{57} - 104 q^{58} - 88 q^{59} - 104 q^{60} - 232 q^{61} - 112 q^{62} - 48 q^{63} - 16 q^{64} - 104 q^{65} - 88 q^{66} - 408 q^{68} - 896 q^{69} - 24 q^{70} - 48 q^{71} + 56 q^{72} - 208 q^{73} - 104 q^{74} + 296 q^{75} - 112 q^{76} - 48 q^{77} - 400 q^{78} - 48 q^{79} - 384 q^{80} - 104 q^{81} + 352 q^{82} - 112 q^{83} + 16 q^{85} - 208 q^{86} - 232 q^{87} - 104 q^{88} - 88 q^{89} + 168 q^{90} - 160 q^{91} + 80 q^{92} - 104 q^{93} - 952 q^{94} - 104 q^{95} + 56 q^{96} - 232 q^{98} - 160 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
3.1 −0.0518910 − 2.77460i −1.24891 − 0.347191i −5.69714 + 0.213172i −0.215359 − 0.00201366i −0.898510 + 3.48324i 1.07528 − 2.41739i 0.575897 + 10.2548i −1.13035 − 0.681102i 0.00558810 + 0.597642i
3.2 −0.0517663 − 2.76794i −2.50484 − 0.696335i −5.66019 + 0.211789i −2.90626 − 0.0271743i −1.79775 + 6.96928i 1.05439 + 2.42657i 0.568773 + 10.1279i 3.21977 + 1.94010i 0.0752298 + 8.04576i
3.3 −0.0489388 − 2.61675i 2.09524 + 0.582468i −4.84638 + 0.181339i −0.437636 − 0.00409200i 1.42163 − 5.51122i −1.80985 − 1.92988i 0.418198 + 7.44671i 1.48119 + 0.892502i 0.0107096 + 1.14538i
3.4 −0.0488991 − 2.61463i 0.925003 + 0.257147i −4.83529 + 0.180924i 1.92587 + 0.0180074i 0.627112 − 2.43111i 2.04890 + 1.67392i 0.416231 + 7.41168i −1.78007 − 1.07260i −0.0470908 − 5.03631i
3.5 −0.0487603 − 2.60721i 2.46220 + 0.684483i −4.79655 + 0.179474i −3.36530 − 0.0314664i 1.66453 − 6.45285i 0.536053 + 2.59088i 0.409382 + 7.28972i 3.02436 + 1.82236i 0.0820538 + 8.77557i
3.6 −0.0477726 − 2.55439i −2.88513 − 0.802055i −4.52405 + 0.169278i 3.75774 + 0.0351359i −1.91093 + 7.40808i −2.17381 + 1.50816i 0.362026 + 6.44648i 5.11111 + 3.07975i −0.0897665 − 9.60044i
3.7 −0.0470515 − 2.51584i 0.337027 + 0.0936921i −4.32861 + 0.161965i 1.42416 + 0.0133162i 0.219856 − 0.852313i −2.54287 + 0.730626i 0.328969 + 5.85783i −2.46476 − 1.48517i −0.0335073 − 3.58357i
3.8 −0.0452482 − 2.41941i 1.58047 + 0.439365i −3.85291 + 0.144166i −2.95867 − 0.0276643i 0.991492 − 3.84370i 1.40413 − 2.24242i 0.251771 + 4.48320i −0.264720 − 0.159509i 0.0669431 + 7.15950i
3.9 −0.0443154 − 2.36954i −1.03103 − 0.286622i −3.61414 + 0.135232i −3.09717 − 0.0289593i −0.633472 + 2.45577i −2.64238 + 0.133576i 0.214830 + 3.82541i −1.58870 − 0.957286i 0.0686323 + 7.34015i
3.10 −0.0425599 − 2.27567i 1.86522 + 0.518523i −3.17826 + 0.118922i 4.18928 + 0.0391708i 1.10060 − 4.26669i 0.971975 − 2.46074i 0.150653 + 2.68263i 0.640599 + 0.385998i −0.0891554 − 9.53508i
3.11 −0.0399745 − 2.13743i −1.91931 − 0.533561i −2.56841 + 0.0961031i −1.21064 − 0.0113198i −1.06373 + 4.12372i −1.69938 − 2.02783i 0.0683492 + 1.21707i 0.829497 + 0.499821i 0.0241995 + 2.58811i
3.12 −0.0397975 − 2.12796i −0.987712 − 0.274580i −2.52805 + 0.0945928i 1.50738 + 0.0140944i −0.544988 + 2.11274i −0.263911 + 2.63256i 0.0632264 + 1.12585i −1.66939 − 1.00591i −0.0299975 − 3.20821i
3.13 −0.0394791 − 2.11094i 3.07337 + 0.854384i −2.45591 + 0.0918938i 2.80072 + 0.0261874i 1.68222 − 6.52143i −0.234792 + 2.63531i 0.0541755 + 0.964684i 6.14605 + 3.70335i −0.0552897 − 5.91318i
3.14 −0.0382995 − 2.04787i −0.378847 − 0.105318i −2.19369 + 0.0820820i −1.59247 − 0.0148900i −0.201168 + 0.779862i 2.56100 + 0.664299i 0.0224205 + 0.399233i −2.43714 − 1.46852i 0.0304980 + 3.26173i
3.15 −0.0382473 − 2.04507i −2.52289 − 0.701353i −2.18227 + 0.0816547i −0.743562 − 0.00695249i −1.33783 + 5.18632i 2.49437 + 0.882121i 0.0210790 + 0.375347i 3.30351 + 1.99056i 0.0142209 + 1.52091i
3.16 −0.0377060 − 2.01613i −2.86914 − 0.797609i −2.06477 + 0.0772581i 1.69594 + 0.0158575i −1.49990 + 5.81464i 1.76440 − 1.97152i 0.00748620 + 0.133304i 5.02621 + 3.02858i −0.0319763 − 3.41984i
3.17 −0.0341225 − 1.82452i 2.62133 + 0.728718i −1.32912 + 0.0497323i 0.0312986 0.000292650i 1.24012 − 4.80754i 2.60394 − 0.468491i −0.0685486 − 1.22062i 3.77075 + 2.27210i −0.000534041 − 0.0571151i
3.18 −0.0328158 − 1.75466i −0.534968 − 0.148719i −1.07914 + 0.0403787i 3.69632 + 0.0345615i −0.243395 + 0.943565i −2.06822 − 1.64999i −0.0905396 − 1.61221i −2.30550 − 1.38920i −0.0606542 − 6.48691i
3.19 −0.0323230 − 1.72830i 0.120484 + 0.0334940i −0.987386 + 0.0369454i 0.0659185 0.000616355i 0.0539934 − 0.209315i 0.605805 − 2.57546i −0.0980793 − 1.74646i −2.55618 − 1.54025i −0.00106543 − 0.113947i
3.20 −0.0292749 − 1.56532i 1.49345 + 0.415174i −0.450775 + 0.0168668i −3.36543 − 0.0314677i 0.606160 − 2.34989i −2.45319 − 0.990896i −0.135969 − 2.42115i −0.511540 − 0.308233i 0.0492656 + 5.26891i
See next 80 embeddings (of 7872 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 3.82
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
17.e odd 16 1 inner
49.h odd 42 1 inner
833.bn even 336 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 833.2.bn.a ✓ 7872
17.e odd 16 1 inner 833.2.bn.a ✓ 7872
49.h odd 42 1 inner 833.2.bn.a ✓ 7872
833.bn even 336 1 inner 833.2.bn.a ✓ 7872
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
833.2.bn.a ✓ 7872 1.a even 1 1 trivial
833.2.bn.a ✓ 7872 17.e odd 16 1 inner
833.2.bn.a ✓ 7872 49.h odd 42 1 inner
833.2.bn.a ✓ 7872 833.bn even 336 1 inner

Hecke kernels

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