Properties

Label 8026.2.a.c
Level $8026$
Weight $2$
Character orbit 8026.a
Self dual yes
Analytic conductor $64.088$
Analytic rank $0$
Dimension $86$
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] = [8026,2,Mod(1,8026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8026, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8026 = 2 \cdot 4013 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8026.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: \(64.0879326623\)
Analytic rank: \(0\)
Dimension: \(86\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 −1.00000 −3.25486 1.00000 3.01406 3.25486 −0.942473 −1.00000 7.59411 −3.01406
1.2 −1.00000 −3.25191 1.00000 −1.61920 3.25191 −4.93737 −1.00000 7.57490 1.61920
1.3 −1.00000 −3.20966 1.00000 0.782750 3.20966 3.68309 −1.00000 7.30189 −0.782750
1.4 −1.00000 −3.19050 1.00000 −0.434778 3.19050 2.23469 −1.00000 7.17932 0.434778
1.5 −1.00000 −3.14403 1.00000 0.849411 3.14403 0.337791 −1.00000 6.88495 −0.849411
1.6 −1.00000 −3.04565 1.00000 −0.405483 3.04565 −0.211812 −1.00000 6.27596 0.405483
1.7 −1.00000 −2.97454 1.00000 −1.53544 2.97454 2.95859 −1.00000 5.84792 1.53544
1.8 −1.00000 −2.68740 1.00000 3.50149 2.68740 −3.96925 −1.00000 4.22214 −3.50149
1.9 −1.00000 −2.64301 1.00000 −0.786430 2.64301 −4.08167 −1.00000 3.98548 0.786430
1.10 −1.00000 −2.62565 1.00000 −4.13736 2.62565 −3.98462 −1.00000 3.89402 4.13736
1.11 −1.00000 −2.61892 1.00000 3.93925 2.61892 4.49129 −1.00000 3.85875 −3.93925
1.12 −1.00000 −2.55894 1.00000 −3.60377 2.55894 −1.20803 −1.00000 3.54817 3.60377
1.13 −1.00000 −2.34399 1.00000 1.04947 2.34399 −2.18495 −1.00000 2.49429 −1.04947
1.14 −1.00000 −2.31833 1.00000 1.68969 2.31833 −0.814652 −1.00000 2.37465 −1.68969
1.15 −1.00000 −2.09967 1.00000 3.00804 2.09967 1.34654 −1.00000 1.40862 −3.00804
1.16 −1.00000 −2.07592 1.00000 1.44155 2.07592 −4.11205 −1.00000 1.30942 −1.44155
1.17 −1.00000 −2.06398 1.00000 −1.63652 2.06398 0.580095 −1.00000 1.26000 1.63652
1.18 −1.00000 −1.90629 1.00000 −3.44864 1.90629 0.576337 −1.00000 0.633932 3.44864
1.19 −1.00000 −1.83924 1.00000 4.20278 1.83924 −0.870895 −1.00000 0.382816 −4.20278
1.20 −1.00000 −1.77113 1.00000 −2.88416 1.77113 −2.34784 −1.00000 0.136917 2.88416
See all 86 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.86
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(4013\) \(-1\)

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 8026.2.a.c 86
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8026.2.a.c 86 1.a even 1 1 trivial