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Properties

Label 833.2.x.a
Level $833$
Weight $2$
Character orbit 833.x
Analytic conductor $6.652$
Analytic rank $0$
Dimension $984$
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(64,833)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(833, base_ring=CyclotomicField(28))
 
chi = DirichletCharacter(H, H._module([20, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("833.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 833 = 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 833.x (of order \(28\), 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: \(984\)
Relative dimension: \(82\) over \(\Q(\zeta_{28})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 984 q - 10 q^{3} + 140 q^{4} - 6 q^{5} - 18 q^{6} - 14 q^{7}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 984 q - 10 q^{3} + 140 q^{4} - 6 q^{5} - 18 q^{6} - 14 q^{7} - 18 q^{10} - 20 q^{11} + 44 q^{12} - 28 q^{13} + 56 q^{14} - 188 q^{16} - 2 q^{17} - 48 q^{18} + 22 q^{20} - 20 q^{21} + 14 q^{22} - 56 q^{23} + 66 q^{24} + 20 q^{27} - 98 q^{28} - 26 q^{29} - 32 q^{31} - 12 q^{33} + 6 q^{34} - 44 q^{35} + 6 q^{37} - 20 q^{38} - 22 q^{39} - 102 q^{40} - 18 q^{41} - 58 q^{44} + 20 q^{45} - 38 q^{46} - 40 q^{47} - 20 q^{48} - 48 q^{50} + 30 q^{51} - 28 q^{52} - 28 q^{54} + 12 q^{55} - 14 q^{56} + 50 q^{57} - 118 q^{58} + 2 q^{61} + 82 q^{62} - 22 q^{63} + 84 q^{64} - 18 q^{65} - 40 q^{67} + 4 q^{68} - 108 q^{69} - 52 q^{71} - 228 q^{72} - 22 q^{73} - 86 q^{74} - 106 q^{75} - 62 q^{78} - 20 q^{79} + 88 q^{80} + 152 q^{81} - 68 q^{82} + 340 q^{84} + 106 q^{85} + 136 q^{86} - 180 q^{88} - 76 q^{89} - 266 q^{90} + 134 q^{91} - 10 q^{92} - 100 q^{95} + 16 q^{96} - 28 q^{97} + 224 q^{98} - 268 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
64.1 −2.69461 − 0.615028i 2.97889 − 0.335640i 5.08074 + 2.44675i 2.64017 − 0.297475i −8.23337 − 0.927678i −0.445563 − 2.60796i −7.86397 − 6.27130i 5.83632 − 1.33210i −7.29718 − 0.822194i
64.2 −2.56375 − 0.585159i −0.604940 + 0.0681603i 4.42846 + 2.13263i 1.97482 − 0.222509i 1.59080 + 0.179240i 2.59207 + 0.530256i −5.99359 − 4.77973i −2.56348 + 0.585097i −5.19314 − 0.585127i
64.3 −2.51514 − 0.574064i 1.87379 − 0.211125i 4.19444 + 2.01994i 0.242284 − 0.0272988i −4.83404 − 0.544665i −1.02776 + 2.43797i −5.35607 − 4.27132i 0.541722 − 0.123645i −0.625049 − 0.0704261i
64.4 −2.51399 − 0.573802i 1.36993 − 0.154354i 4.18895 + 2.01729i −2.87599 + 0.324046i −3.53256 − 0.398024i 2.27437 + 1.35176i −5.34133 − 4.25957i −1.07190 + 0.244653i 7.41615 + 0.835599i
64.5 −2.48897 − 0.568092i −0.347013 + 0.0390990i 4.07032 + 1.96016i 3.42677 − 0.386104i 0.885918 + 0.0998190i −2.25105 + 1.39024i −5.02536 − 4.00759i −2.80589 + 0.640427i −8.74848 − 0.985717i
64.6 −2.47556 − 0.565031i −2.77902 + 0.313120i 4.00721 + 1.92977i −0.132416 + 0.0149196i 7.05656 + 0.795083i −2.45970 + 0.974612i −4.85924 − 3.87511i 4.70012 − 1.07277i 0.336233 + 0.0378844i
64.7 −2.39896 − 0.547546i −1.12103 + 0.126310i 3.65325 + 1.75931i −1.50845 + 0.169962i 2.75846 + 0.310804i −1.77985 − 1.95758i −3.95305 − 3.15245i −1.68403 + 0.384368i 3.71177 + 0.418217i
64.8 −2.32288 − 0.530182i −1.87391 + 0.211139i 3.31274 + 1.59533i −3.75556 + 0.423150i 4.46481 + 0.503063i −0.244728 + 2.63441i −3.12367 − 2.49105i 0.542171 − 0.123747i 8.94806 + 1.00820i
64.9 −2.26998 − 0.518108i 2.38731 − 0.268985i 3.08242 + 1.48442i −3.56553 + 0.401739i −5.55850 − 0.626292i 1.38828 − 2.25226i −2.58719 − 2.06321i 2.70210 − 0.616737i 8.30183 + 0.935391i
64.10 −2.23745 − 0.510684i −2.88550 + 0.325118i 2.94347 + 1.41750i −0.383906 + 0.0432558i 6.62221 + 0.746144i 1.46554 − 2.20277i −2.27338 − 1.81296i 5.29564 − 1.20869i 0.881062 + 0.0992719i
64.11 −2.21066 − 0.504569i 2.00309 − 0.225694i 2.83049 + 1.36309i −1.29914 + 0.146378i −4.54204 − 0.511765i −2.57779 − 0.595814i −2.02386 − 1.61397i 1.03666 − 0.236611i 2.94581 + 0.331913i
64.12 −2.15478 − 0.491814i −2.27479 + 0.256308i 2.59925 + 1.25173i 4.31041 − 0.485667i 5.02773 + 0.566489i −0.156718 − 2.64111i −1.52920 − 1.21949i 2.18420 − 0.498530i −9.52685 − 1.07342i
64.13 −2.06359 − 0.471001i 0.471490 − 0.0531242i 2.23463 + 1.07614i 0.647015 − 0.0729010i −0.997984 − 0.112446i 2.48354 − 0.912147i −0.794750 − 0.633792i −2.70530 + 0.617468i −1.36951 − 0.154307i
64.14 −1.95409 − 0.446009i −1.06482 + 0.119976i 1.81762 + 0.875322i −1.39775 + 0.157488i 2.13427 + 0.240475i 0.926663 + 2.47816i −0.0272835 − 0.0217579i −1.80534 + 0.412056i 2.80157 + 0.315662i
64.15 −1.92932 − 0.440354i 3.33325 − 0.375567i 1.72642 + 0.831399i −0.419579 + 0.0472752i −6.59628 − 0.743223i −0.0636170 + 2.64499i 0.129687 + 0.103422i 8.04473 − 1.83616i 0.830318 + 0.0935544i
64.16 −1.91086 − 0.436141i −0.149694 + 0.0168665i 1.65922 + 0.799038i −3.02677 + 0.341035i 0.293400 + 0.0330582i −2.08018 − 1.63488i 0.242739 + 0.193578i −2.90266 + 0.662513i 5.93247 + 0.668428i
64.17 −1.89923 − 0.433486i 2.35724 − 0.265597i 1.61722 + 0.778811i 3.41325 − 0.384580i −4.59207 − 0.517402i 2.64131 + 0.153284i 0.312265 + 0.249023i 2.56127 − 0.584593i −6.64924 − 0.749190i
64.18 −1.68339 − 0.384223i −0.841670 + 0.0948334i 0.884241 + 0.425828i 2.29777 − 0.258896i 1.45330 + 0.163747i 0.247371 + 2.63416i 1.37504 + 1.09656i −2.22537 + 0.507926i −3.96752 − 0.447032i
64.19 −1.64718 − 0.375959i 0.812063 − 0.0914975i 0.769925 + 0.370777i 2.72248 − 0.306750i −1.37201 − 0.154589i −1.13012 − 2.39225i 1.51306 + 1.20663i −2.27371 + 0.518959i −4.59975 − 0.518267i
64.20 −1.57666 − 0.359863i −2.55012 + 0.287330i 0.554421 + 0.266995i −0.938827 + 0.105780i 4.12408 + 0.464672i 2.62434 + 0.335923i 1.75071 + 1.39615i 3.49578 − 0.797890i 1.51828 + 0.171069i
See next 80 embeddings (of 984 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 64.82
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
17.c even 4 1 inner
49.e even 7 1 inner
833.x even 28 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 833.2.x.a ✓ 984
17.c even 4 1 inner 833.2.x.a ✓ 984
49.e even 7 1 inner 833.2.x.a ✓ 984
833.x even 28 1 inner 833.2.x.a ✓ 984
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
833.2.x.a ✓ 984 1.a even 1 1 trivial
833.2.x.a ✓ 984 17.c even 4 1 inner
833.2.x.a ✓ 984 49.e even 7 1 inner
833.2.x.a ✓ 984 833.x even 28 1 inner

Hecke kernels

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