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Properties

Label 8029.2.a.h
Level $8029$
Weight $2$
Character orbit 8029.a
Self dual yes
Analytic conductor $64.112$
Analytic rank $0$
Dimension $71$
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] = [8029,2,Mod(1,8029)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8029, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8029.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8029 = 7 \cdot 31 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8029.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: \(64.1118877829\)
Analytic rank: \(0\)
Dimension: \(71\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 71 q + 6 q^{2} + 8 q^{3} + 78 q^{4} + 5 q^{6} - 71 q^{7} + 18 q^{8} + 87 q^{9} + 4 q^{10} + 57 q^{11} + 21 q^{12} - 20 q^{13} - 6 q^{14} + 22 q^{15} + 88 q^{16} - 19 q^{17} + q^{18} + 23 q^{19} + 25 q^{20} - 8 q^{21} + 18 q^{22} + 34 q^{23} + 15 q^{24} + 81 q^{25} - 13 q^{26} + 20 q^{27} - 78 q^{28} + 16 q^{29} + 6 q^{30} - 71 q^{31} + 47 q^{32} - 16 q^{33} + 32 q^{34} + 125 q^{36} + 71 q^{37} + 13 q^{38} + 30 q^{39} + 31 q^{40} + 17 q^{41} - 5 q^{42} + 38 q^{43} + 80 q^{44} - q^{45} + 26 q^{46} + 32 q^{47} + 61 q^{48} + 71 q^{49} + 47 q^{50} + 73 q^{51} - 23 q^{52} + 31 q^{53} + 47 q^{54} + 11 q^{55} - 18 q^{56} + 17 q^{57} - 2 q^{58} + 97 q^{59} + 103 q^{60} - q^{61} - 6 q^{62} - 87 q^{63} + 100 q^{64} + 46 q^{65} + 43 q^{66} + 75 q^{67} - 43 q^{68} + 10 q^{69} - 4 q^{70} + 131 q^{71} - 11 q^{72} - 15 q^{73} + 6 q^{74} + 76 q^{75} + 41 q^{76} - 57 q^{77} + 89 q^{78} + 8 q^{79} + 10 q^{80} + 171 q^{81} + 14 q^{82} + 18 q^{83} - 21 q^{84} + 47 q^{85} + 90 q^{86} - 59 q^{87} + 13 q^{88} + 18 q^{89} + 69 q^{90} + 20 q^{91} + 110 q^{92} - 8 q^{93} + 39 q^{94} + 72 q^{95} + 100 q^{96} + 23 q^{97} + 6 q^{98} + 168 q^{99}+O(q^{100}) \) 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 −2.78017 2.03796 5.72934 0.445141 −5.66588 −1.00000 −10.3682 1.15330 −1.23757
1.2 −2.69431 0.251057 5.25931 0.178464 −0.676426 −1.00000 −8.78160 −2.93697 −0.480839
1.3 −2.64917 −3.09220 5.01811 0.332247 8.19178 −1.00000 −7.99549 6.56173 −0.880180
1.4 −2.63529 −1.71677 4.94476 −3.15507 4.52418 −1.00000 −7.76032 −0.0527133 8.31452
1.5 −2.40369 2.90614 3.77774 −0.715086 −6.98547 −1.00000 −4.27315 5.44566 1.71885
1.6 −2.38302 3.20550 3.67879 −2.71243 −7.63877 −1.00000 −4.00058 7.27524 6.46378
1.7 −2.31484 −2.30235 3.35848 0.0649698 5.32957 −1.00000 −3.14465 2.30082 −0.150395
1.8 −2.30726 1.92904 3.32347 4.29364 −4.45079 −1.00000 −3.05358 0.721177 −9.90655
1.9 −2.28647 −0.837618 3.22797 2.08578 1.91519 −1.00000 −2.80772 −2.29840 −4.76908
1.10 −2.10847 1.17312 2.44565 1.33093 −2.47348 −1.00000 −0.939631 −1.62379 −2.80623
1.11 −2.07728 −3.28410 2.31510 0.477215 6.82201 −1.00000 −0.654560 7.78532 −0.991310
1.12 −2.06856 3.20449 2.27895 4.21324 −6.62868 −1.00000 −0.577029 7.26874 −8.71536
1.13 −2.02141 0.0362870 2.08609 −2.43486 −0.0733508 −1.00000 −0.174025 −2.99868 4.92185
1.14 −2.02044 −0.0586839 2.08218 2.29077 0.118567 −1.00000 −0.166030 −2.99656 −4.62836
1.15 −1.95127 1.43500 1.80747 −4.32832 −2.80008 −1.00000 0.375685 −0.940772 8.44573
1.16 −1.86191 −1.06463 1.46672 −1.77871 1.98225 −1.00000 0.992917 −1.86656 3.31181
1.17 −1.56268 −3.23783 0.441960 −3.23512 5.05968 −1.00000 2.43471 7.48352 5.05544
1.18 −1.50294 0.107359 0.258826 3.46915 −0.161355 −1.00000 2.61688 −2.98847 −5.21392
1.19 −1.49331 −1.98225 0.229971 2.93836 2.96012 −1.00000 2.64320 0.929333 −4.38788
1.20 −1.38552 1.91783 −0.0803442 −0.654097 −2.65719 −1.00000 2.88235 0.678074 0.906262
See all 71 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.71
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(7\) \(1\)
\(31\) \(1\)
\(37\) \(-1\)

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 8029.2.a.h ✓ 71
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8029.2.a.h ✓ 71 1.a even 1 1 trivial