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Properties

Label 83.20.a.b
Level $83$
Weight $20$
Character orbit 83.a
Self dual yes
Analytic conductor $189.918$
Analytic rank $0$
Dimension $68$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [83,20,Mod(1,83)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(83, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 20, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("83.1");
 
S:= CuspForms(chi, 20);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 83 \)
Weight: \( k \) \(=\) \( 20 \)
Character orbit: \([\chi]\) \(=\) 83.a (trivial)

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: yes
Analytic conductor: \(189.917858142\)
Analytic rank: \(0\)
Dimension: \(68\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 68 q + 1079 q^{2} + 23899 q^{3} + 19500741 q^{4} + 13265118 q^{5} + 42450825 q^{6} + 362030721 q^{7} + 1590767103 q^{8} + 27974384947 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 68 q + 1079 q^{2} + 23899 q^{3} + 19500741 q^{4} + 13265118 q^{5} + 42450825 q^{6} + 362030721 q^{7} + 1590767103 q^{8} + 27974384947 q^{9} + 4541061765 q^{10} - 7766081849 q^{11} + 35427774439 q^{12} + 137031576394 q^{13} + 88337602596 q^{14} + 563456876474 q^{15} + 6145611211445 q^{16} - 250615438977 q^{17} + 1282938474544 q^{18} + 3269128227210 q^{19} + 7781297130583 q^{20} - 3090318180458 q^{21} + 47108253271187 q^{22} + 6234930110521 q^{23} - 74083740826973 q^{24} + 301949991516930 q^{25} - 116378577289447 q^{26} + 121284760778194 q^{27} + 445808465095352 q^{28} + 387926775972881 q^{29} + 15\!\cdots\!92 q^{30}+ \cdots - 10\!\cdots\!70 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −1406.68 44622.8 1.45445e6 4.67115e6 −6.27698e7 −1.80894e8 −1.30843e9 8.28935e8 −6.57079e9
1.2 −1405.53 −5401.91 1.45122e6 −1.69772e6 7.59253e6 1.13977e8 −1.30282e9 −1.13308e9 2.38619e9
1.3 −1393.83 48220.2 1.41849e6 −2.55588e6 −6.72109e7 1.26360e8 −1.24637e9 1.16292e9 3.56248e9
1.4 −1339.92 27973.4 1.27109e6 115774. −3.74821e7 −1.00292e8 −1.00065e9 −3.79749e8 −1.55127e8
1.5 −1270.10 −64315.3 1.08886e6 2.24403e6 8.16868e7 1.96978e8 −7.17064e8 2.97420e9 −2.85014e9
1.6 −1241.67 −11354.3 1.01745e6 −5.56844e6 1.40983e7 −1.64215e8 −6.12347e8 −1.03334e9 6.91416e9
1.7 −1212.04 −46801.6 944741. 752568. 5.67252e7 −3.32672e7 −5.09604e8 1.02813e9 −9.12138e8
1.8 −1193.33 11217.5 899747. 4.03430e6 −1.33862e7 −1.10188e8 −4.48046e8 −1.03643e9 −4.81425e9
1.9 −1115.58 52428.9 720233. 5.61722e6 −5.84887e7 8.43113e7 −2.18593e8 1.58652e9 −6.26646e9
1.10 −1108.33 −56818.5 704109. −251183. 6.29737e7 −1.99899e8 −1.99302e8 2.06608e9 2.78394e8
1.11 −1090.50 6753.58 664900. −7.27672e6 −7.36477e6 1.92343e8 −1.53338e8 −1.11665e9 7.93525e9
1.12 −1044.86 −38596.7 567442. 4.62787e6 4.03281e7 1.62780e8 −4.50898e7 3.27445e8 −4.83547e9
1.13 −1016.97 −30237.6 509944. −852893. 3.07508e7 9.76000e7 1.45870e7 −2.47947e8 8.67368e8
1.14 −939.248 17840.9 357899. −157425. −1.67570e7 1.47233e7 1.56280e8 −8.43964e8 1.47861e8
1.15 −894.814 43212.2 276405. −2.69096e6 −3.86669e7 −1.21053e8 2.21809e8 7.05035e8 2.40791e9
1.16 −828.532 35120.0 162178. 6.12064e6 −2.90981e7 −6.24540e7 3.00020e8 7.11557e7 −5.07115e9
1.17 −827.839 −48005.9 161030. −6.92312e6 3.97411e7 1.86849e7 3.00719e8 1.14230e9 5.73123e9
1.18 −810.730 −58336.7 132995. 8.19028e6 4.72953e7 −4.34327e7 3.17233e8 2.24091e9 −6.64010e9
1.19 −779.214 53737.2 82887.0 601921. −4.18728e7 1.69913e8 3.43946e8 1.72543e9 −4.69025e8
1.20 −772.854 −1980.97 73015.6 −6.10764e6 1.53100e6 −2.00381e7 3.48768e8 −1.15834e9 4.72031e9
See all 68 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.68
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(83\) \(1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 83.20.a.b ✓ 68
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
83.20.a.b ✓ 68 1.a even 1 1 trivial