Properties

Label 8026.2.a.d
Level $8026$
Weight $2$
Character orbit 8026.a
Self dual yes
Analytic conductor $64.088$
Analytic rank $0$
Dimension $96$
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: \(96\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 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 −3.38260 1.00000 3.86577 −3.38260 1.67092 1.00000 8.44195 3.86577
1.2 1.00000 −3.34006 1.00000 0.570499 −3.34006 −3.09347 1.00000 8.15597 0.570499
1.3 1.00000 −3.28199 1.00000 4.44756 −3.28199 −4.87209 1.00000 7.77147 4.44756
1.4 1.00000 −3.27254 1.00000 −0.667760 −3.27254 −3.79895 1.00000 7.70950 −0.667760
1.5 1.00000 −3.25028 1.00000 −3.55308 −3.25028 1.03732 1.00000 7.56432 −3.55308
1.6 1.00000 −3.15603 1.00000 0.126707 −3.15603 5.16404 1.00000 6.96052 0.126707
1.7 1.00000 −2.94262 1.00000 −2.75708 −2.94262 −0.162948 1.00000 5.65901 −2.75708
1.8 1.00000 −2.86733 1.00000 −3.62078 −2.86733 −3.60760 1.00000 5.22157 −3.62078
1.9 1.00000 −2.84755 1.00000 2.66905 −2.84755 0.0156637 1.00000 5.10852 2.66905
1.10 1.00000 −2.83728 1.00000 3.92961 −2.83728 4.49024 1.00000 5.05014 3.92961
1.11 1.00000 −2.81326 1.00000 −0.734328 −2.81326 −3.92682 1.00000 4.91446 −0.734328
1.12 1.00000 −2.75991 1.00000 1.94869 −2.75991 −1.07781 1.00000 4.61711 1.94869
1.13 1.00000 −2.59431 1.00000 −1.49267 −2.59431 1.08103 1.00000 3.73042 −1.49267
1.14 1.00000 −2.44392 1.00000 2.01179 −2.44392 1.54759 1.00000 2.97273 2.01179
1.15 1.00000 −2.41544 1.00000 3.01333 −2.41544 −2.26454 1.00000 2.83435 3.01333
1.16 1.00000 −2.39250 1.00000 1.27700 −2.39250 3.72505 1.00000 2.72406 1.27700
1.17 1.00000 −2.32778 1.00000 2.23848 −2.32778 3.76217 1.00000 2.41856 2.23848
1.18 1.00000 −2.32502 1.00000 −1.28151 −2.32502 −2.20923 1.00000 2.40572 −1.28151
1.19 1.00000 −2.26664 1.00000 −3.59818 −2.26664 5.23582 1.00000 2.13767 −3.59818
1.20 1.00000 −2.21370 1.00000 0.840207 −2.21370 −5.05822 1.00000 1.90049 0.840207
See all 96 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.96
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.d 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8026.2.a.d 96 1.a even 1 1 trivial