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Properties

Label 833.2.bg.a
Level $833$
Weight $2$
Character orbit 833.bg
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(4,833)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(833, base_ring=CyclotomicField(84))
 
chi = DirichletCharacter(H, H._module([20, 63]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("833.4");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 833.bg (of order \(84\), 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 \(\Q(\zeta_{84})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{84}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1968 q - 26 q^{3} - 212 q^{4} - 24 q^{5} - 12 q^{6} - 22 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 1968 q - 26 q^{3} - 212 q^{4} - 24 q^{5} - 12 q^{6} - 22 q^{7} - 18 q^{10} - 10 q^{11} - 122 q^{12} - 56 q^{13} - 68 q^{14} + 92 q^{16} - 22 q^{17} - 52 q^{20} - 52 q^{21} - 44 q^{22} + 14 q^{23} - 132 q^{24} - 86 q^{27} + 38 q^{28} - 4 q^{29} - 16 q^{31} - 36 q^{33} - 36 q^{34} - 100 q^{35} - 18 q^{37} - 76 q^{38} - 32 q^{39} + 24 q^{40} - 72 q^{41} + 10 q^{44} + 124 q^{45} - 28 q^{46} + 40 q^{47} - 124 q^{48} - 96 q^{50} - 6 q^{51} - 68 q^{52} + 10 q^{54} - 168 q^{55} + 14 q^{56} - 80 q^{57} - 164 q^{58} + 4 q^{61} - 52 q^{62} - 98 q^{63} + 264 q^{64} - 30 q^{65} - 20 q^{67} - 22 q^{68} + 144 q^{69} + 22 q^{71} - 36 q^{72} - 32 q^{73} - 52 q^{74} + 64 q^{75} + 104 q^{78} - 10 q^{79} - 40 q^{80} - 80 q^{81} - 136 q^{82} - 340 q^{84} - 136 q^{85} + 320 q^{86} - 456 q^{88} - 8 q^{89} + 164 q^{90} - 152 q^{91} - 20 q^{92} - 314 q^{95} + 692 q^{96} + 28 q^{97} + 208 q^{98} + 196 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
4.1 −1.54470 + 2.26565i −1.55261 + 0.0580947i −2.01641 − 5.13774i 1.08136 − 2.04604i 2.26669 − 3.60742i −0.388369 − 2.61709i 9.40833 + 2.14739i −0.584376 + 0.0437929i 2.96523 + 5.61049i
4.2 −1.51602 + 2.22360i 0.102997 − 0.00385387i −1.91538 − 4.88030i −0.707387 + 1.33844i −0.147576 + 0.234866i 2.49264 + 0.886990i 8.50808 + 1.94191i −2.98102 + 0.223396i −1.90374 − 3.60205i
4.3 −1.50031 + 2.20055i −0.540185 + 0.0202123i −1.86081 − 4.74127i −1.94112 + 3.67278i 0.765967 − 1.21903i −2.47501 + 0.935065i 8.03207 + 1.83327i −2.70022 + 0.202354i −5.16986 − 9.78185i
4.4 −1.49563 + 2.19369i −3.19903 + 0.119699i −1.84468 − 4.70018i −0.0387773 + 0.0733702i 4.52199 − 7.19671i 0.706303 + 2.54973i 7.89279 + 1.80148i 7.22784 − 0.541651i −0.102955 − 0.194800i
4.5 −1.43886 + 2.11042i 2.30173 − 0.0861247i −1.65287 − 4.21145i 1.61068 − 3.04756i −3.13011 + 4.98154i 2.59547 + 0.513350i 6.28576 + 1.43468i 2.29894 − 0.172282i 4.11408 + 7.78423i
4.6 −1.43303 + 2.10187i −0.616084 + 0.0230522i −1.63361 − 4.16236i 1.23869 − 2.34372i 0.834416 − 1.32796i −1.19775 + 2.35911i 6.12952 + 1.39902i −2.61258 + 0.195786i 3.15112 + 5.96221i
4.7 −1.38554 + 2.03221i 3.22258 − 0.120580i −1.47948 − 3.76966i −1.48926 + 2.81781i −4.21996 + 6.71603i 0.605653 + 2.57550i 4.91478 + 1.12177i 7.37885 − 0.552969i −3.66296 − 6.93067i
4.8 −1.36042 + 1.99536i 0.843293 − 0.0315538i −1.40006 − 3.56730i 0.720251 − 1.36278i −1.08427 + 1.72560i −0.904516 − 2.48633i 4.31382 + 0.984601i −2.28146 + 0.170972i 1.73940 + 3.29111i
4.9 −1.32678 + 1.94603i 2.11869 − 0.0792758i −1.29600 − 3.30215i 0.147607 − 0.279287i −2.65676 + 4.22821i −1.71214 + 2.01707i 3.55312 + 0.810976i 1.49095 − 0.111731i 0.347657 + 0.657800i
4.10 −1.28514 + 1.88496i 2.64622 − 0.0990145i −1.17079 − 2.98314i −0.662691 + 1.25387i −3.21413 + 5.11526i 1.28256 − 2.31410i 2.67938 + 0.611550i 4.00105 − 0.299837i −1.51184 − 2.86055i
4.11 −1.27639 + 1.87212i −2.12547 + 0.0795293i −1.14498 − 2.91737i −1.43533 + 2.71578i 2.56404 − 4.08064i 1.45319 − 2.21093i 2.50507 + 0.571765i 1.51967 − 0.113883i −3.25223 − 6.15352i
4.12 −1.24173 + 1.82128i −2.90140 + 0.108563i −1.04449 − 2.66131i −0.440122 + 0.832752i 3.40502 − 5.41905i −2.36310 − 1.18985i 1.84590 + 0.421314i 5.41470 − 0.405775i −0.970161 − 1.83564i
4.13 −1.20693 + 1.77024i 0.324047 − 0.0121250i −0.946384 − 2.41135i −0.345436 + 0.653597i −0.369637 + 0.588274i 2.42850 − 1.04996i 1.23326 + 0.281483i −2.88675 + 0.216332i −0.740105 − 1.40035i
4.14 −1.19976 + 1.75973i 0.843756 − 0.0315711i −0.926536 − 2.36077i −0.444945 + 0.841876i −0.956751 + 1.52266i −2.57808 − 0.594560i 1.11313 + 0.254065i −2.28068 + 0.170914i −0.947647 − 1.79304i
4.15 −1.11942 + 1.64189i −2.76985 + 0.103640i −0.712010 − 1.81417i 1.88408 − 3.56485i 2.93045 − 4.66379i 2.30566 − 1.29767i −0.0990140 − 0.0225993i 4.66969 − 0.349945i 3.74400 + 7.08400i
4.16 −1.11379 + 1.63363i −2.38829 + 0.0893636i −0.697543 − 1.77731i 0.254391 − 0.481332i 2.51407 − 4.00113i −0.476317 + 2.60252i −0.174847 − 0.0399078i 2.70434 − 0.202662i 0.502981 + 0.951686i
4.17 −1.00745 + 1.47766i −0.0971428 + 0.00363483i −0.437834 − 1.11558i −0.861116 + 1.62931i 0.0924955 − 0.147206i 1.65463 + 2.06451i −1.39761 − 0.318995i −2.98219 + 0.223484i −1.54003 − 2.91388i
4.18 −0.999087 + 1.46539i −1.12694 + 0.0421672i −0.418516 − 1.06636i 1.09555 − 2.07288i 1.06412 − 1.69354i 2.61893 + 0.375793i −1.47743 − 0.337215i −1.72339 + 0.129150i 1.94303 + 3.67639i
4.19 −0.975067 + 1.43016i 3.32060 − 0.124248i −0.363923 − 0.927260i 1.04050 − 1.96872i −3.06012 + 4.87015i −0.926203 − 2.47834i −1.69408 − 0.386663i 8.01936 − 0.600968i 1.80103 + 3.40772i
4.20 −0.935024 + 1.37143i 1.88902 − 0.0706823i −0.275864 − 0.702890i 1.24739 − 2.36017i −1.66935 + 2.65675i 0.223003 + 2.63634i −2.01456 − 0.459809i 0.571804 − 0.0428508i 2.07047 + 3.91752i
See next 80 embeddings (of 1968 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 4.82
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
17.c even 4 1 inner
49.g even 21 1 inner
833.bg even 84 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 833.2.bg.a ✓ 1968
17.c even 4 1 inner 833.2.bg.a ✓ 1968
49.g even 21 1 inner 833.2.bg.a ✓ 1968
833.bg even 84 1 inner 833.2.bg.a ✓ 1968
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
833.2.bg.a ✓ 1968 1.a even 1 1 trivial
833.2.bg.a ✓ 1968 17.c even 4 1 inner
833.2.bg.a ✓ 1968 49.g even 21 1 inner
833.2.bg.a ✓ 1968 833.bg even 84 1 inner

Hecke kernels

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