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Properties

Label 483.2.q.d
Level $483$
Weight $2$
Character orbit 483.q
Analytic conductor $3.857$
Analytic rank $0$
Dimension $60$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [483,2,Mod(64,483)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(483, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 0, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("483.64");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.q (of order \(11\), degree \(10\), 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: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(6\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 60 q - q^{2} + 6 q^{3} - 3 q^{4} - 13 q^{5} + 12 q^{6} - 6 q^{7} + 25 q^{8} - 6 q^{9} + 5 q^{11} + 3 q^{12} + 22 q^{13} - q^{14} + 2 q^{15} - 27 q^{16} + q^{17} - q^{18} + 20 q^{19} - 75 q^{20} + 6 q^{21} - 16 q^{22} - 9 q^{23} - 36 q^{24} - 15 q^{25} - 16 q^{26} + 6 q^{27} - 14 q^{28} - 3 q^{29} + 17 q^{31} - 73 q^{32} - 5 q^{33} + 55 q^{34} - 2 q^{35} - 14 q^{36} + 56 q^{37} - 22 q^{38} - 22 q^{39} - 37 q^{40} - 18 q^{41} + 12 q^{42} - 19 q^{43} - 12 q^{44} + 20 q^{45} - 45 q^{46} + 42 q^{47} - 28 q^{48} - 6 q^{49} - 42 q^{50} - q^{51} + 76 q^{52} - 11 q^{53} - 10 q^{54} - 61 q^{55} + 3 q^{56} + 24 q^{57} - 78 q^{58} + 38 q^{59} + 31 q^{60} + 5 q^{61} + 69 q^{62} - 6 q^{63} - 27 q^{64} + 51 q^{65} + 49 q^{66} - 27 q^{67} + 112 q^{68} - 13 q^{69} + 22 q^{70} - 4 q^{71} + 25 q^{72} + 48 q^{73} - 62 q^{74} + 26 q^{75} - 85 q^{76} - 28 q^{77} - 6 q^{78} - 6 q^{79} + 169 q^{80} - 6 q^{81} - 200 q^{82} - 6 q^{83} + 3 q^{84} - 21 q^{85} - 180 q^{86} + 14 q^{87} + 211 q^{88} - 57 q^{89} - 22 q^{91} + 49 q^{92} - 50 q^{93} + 16 q^{94} + 56 q^{95} + 7 q^{96} - 52 q^{97} - 12 q^{98} + 5 q^{99}+O(q^{100}) \) 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 −2.35051 − 0.690173i 0.654861 − 0.755750i 3.36607 + 2.16324i −0.0495443 + 0.344588i −2.06086 + 1.32443i 0.415415 + 0.909632i −3.21050 − 3.70511i −0.142315 − 0.989821i 0.354280 − 0.775765i
64.2 −1.03092 − 0.302706i 0.654861 − 0.755750i −0.711340 − 0.457151i −0.107286 + 0.746189i −0.903879 + 0.580888i 0.415415 + 0.909632i 2.00217 + 2.31063i −0.142315 − 0.989821i 0.336479 − 0.736786i
64.3 −0.0618105 − 0.0181492i 0.654861 − 0.755750i −1.67902 − 1.07904i −0.424340 + 2.95135i −0.0541936 + 0.0348281i 0.415415 + 0.909632i 0.168569 + 0.194540i −0.142315 − 0.989821i 0.0797933 − 0.174723i
64.4 1.04309 + 0.306279i 0.654861 − 0.755750i −0.688274 − 0.442327i 0.159962 − 1.11256i 0.914550 − 0.587746i 0.415415 + 0.909632i −2.00629 − 2.31538i −0.142315 − 0.989821i 0.507608 − 1.11151i
64.5 2.07162 + 0.608284i 0.654861 − 0.755750i 2.23911 + 1.43899i −0.483629 + 3.36371i 1.81634 − 1.16729i 0.415415 + 0.909632i 0.935489 + 1.07961i −0.142315 − 0.989821i −3.04799 + 6.67417i
64.6 2.24006 + 0.657740i 0.654861 − 0.755750i 2.90273 + 1.86547i 0.461461 − 3.20953i 1.96401 − 1.26219i 0.415415 + 0.909632i 2.21758 + 2.55922i −0.142315 − 0.989821i 3.14474 − 6.88602i
85.1 −1.76537 + 2.03734i −0.841254 + 0.540641i −0.749611 − 5.21366i −1.11741 − 2.44678i 0.383651 − 2.66835i −0.959493 + 0.281733i 7.40965 + 4.76189i 0.415415 − 0.909632i 6.95754 + 2.04292i
85.2 −1.19069 + 1.37413i −0.841254 + 0.540641i −0.185857 − 1.29267i −0.605948 − 1.32684i 0.258761 − 1.79972i −0.959493 + 0.281733i −1.06160 − 0.682248i 0.415415 − 0.909632i 2.54474 + 0.747203i
85.3 −1.03904 + 1.19912i −0.841254 + 0.540641i −0.0736471 − 0.512227i 0.945752 + 2.07091i 0.225805 − 1.57051i −0.959493 + 0.281733i −1.97883 − 1.27171i 0.415415 − 0.909632i −3.46594 − 1.01769i
85.4 −0.247496 + 0.285625i −0.841254 + 0.540641i 0.264302 + 1.83826i 1.62071 + 3.54886i 0.0537860 − 0.374090i −0.959493 + 0.281733i −1.22635 − 0.788126i 0.415415 − 0.909632i −1.41476 − 0.415412i
85.5 0.765301 − 0.883205i −0.841254 + 0.540641i 0.0902651 + 0.627808i −0.487321 − 1.06708i −0.166316 + 1.15675i −0.959493 + 0.281733i 2.58982 + 1.66438i 0.415415 − 0.909632i −1.31540 − 0.386237i
85.6 1.53423 − 1.77059i −0.841254 + 0.540641i −0.496516 − 3.45335i −0.667274 − 1.46113i −0.333420 + 2.31898i −0.959493 + 0.281733i −2.93441 − 1.88583i 0.415415 − 0.909632i −3.61081 − 1.06023i
127.1 −2.13310 + 1.37086i 0.142315 − 0.989821i 1.84002 − 4.02908i −1.89262 + 0.555724i 1.05333 + 2.30648i −0.654861 − 0.755750i 0.876645 + 6.09720i −0.959493 − 0.281733i 3.27533 − 3.77993i
127.2 −1.49352 + 0.959824i 0.142315 − 0.989821i 0.478496 − 1.04776i 1.94954 − 0.572436i 0.737505 + 1.61491i −0.654861 − 0.755750i −0.214292 − 1.49043i −0.959493 − 0.281733i −2.36223 + 2.72616i
127.3 −0.502226 + 0.322761i 0.142315 − 0.989821i −0.682774 + 1.49507i −0.741298 + 0.217665i 0.248001 + 0.543047i −0.654861 − 0.755750i −0.309565 − 2.15307i −0.959493 − 0.281733i 0.302045 − 0.348578i
127.4 −0.112067 + 0.0720210i 0.142315 − 0.989821i −0.823458 + 1.80312i −0.784721 + 0.230415i 0.0553392 + 0.121176i −0.654861 − 0.755750i −0.0754970 − 0.525093i −0.959493 − 0.281733i 0.0713466 − 0.0823383i
127.5 1.84770 − 1.18744i 0.142315 − 0.989821i 1.17314 − 2.56882i 2.35208 − 0.690633i −0.912403 − 1.99788i −0.654861 − 0.755750i −0.257569 − 1.79143i −0.959493 − 0.281733i 3.52585 − 4.06905i
127.6 2.29607 − 1.47560i 0.142315 − 0.989821i 2.26374 − 4.95689i −3.38655 + 0.994380i −1.13381 − 2.48270i −0.654861 − 0.755750i −1.33981 − 9.31861i −0.959493 − 0.281733i −6.30846 + 7.28035i
169.1 −0.401532 + 2.79272i −0.415415 − 0.909632i −5.71907 − 1.67927i −1.39224 − 1.60673i 2.70715 − 0.794891i 0.841254 + 0.540641i 4.64198 − 10.1645i −0.654861 + 0.755750i 5.04616 − 3.24297i
169.2 −0.275145 + 1.91367i −0.415415 − 0.909632i −1.66745 − 0.489608i −1.20808 − 1.39419i 1.85504 − 0.544688i 0.841254 + 0.540641i −0.210547 + 0.461033i −0.654861 + 0.755750i 3.00043 − 1.92826i
See all 60 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 64.6
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.c even 11 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 483.2.q.d ✓ 60
23.c even 11 1 inner 483.2.q.d ✓ 60
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
483.2.q.d ✓ 60 1.a even 1 1 trivial
483.2.q.d ✓ 60 23.c even 11 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{60} + T_{2}^{59} + 8 T_{2}^{58} - 14 T_{2}^{57} + 50 T_{2}^{56} - 20 T_{2}^{55} + 729 T_{2}^{54} + \cdots + 59049 \) acting on \(S_{2}^{\mathrm{new}}(483, [\chi])\). Copy content Toggle raw display