↑

Properties

Label 8029.2.a.b
Level $8029$
Weight $2$
Character orbit 8029.a
Self dual yes
Analytic conductor $64.112$
Analytic rank $1$
Dimension $64$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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: \(1\)
Dimension: \(64\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 64 q - 5 q^{2} - 18 q^{3} + 57 q^{4} - 26 q^{5} - 13 q^{6} + 64 q^{7} - 15 q^{8} + 56 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 64 q - 5 q^{2} - 18 q^{3} + 57 q^{4} - 26 q^{5} - 13 q^{6} + 64 q^{7} - 15 q^{8} + 56 q^{9} - 14 q^{10} - 37 q^{11} - 27 q^{12} - 18 q^{13} - 5 q^{14} + 6 q^{15} + 39 q^{16} - 27 q^{17} - 32 q^{18} - 27 q^{19} - 55 q^{20} - 18 q^{21} + 2 q^{22} - 10 q^{23} - 39 q^{24} + 58 q^{25} - 47 q^{26} - 66 q^{27} + 57 q^{28} + 4 q^{29} + 14 q^{30} - 64 q^{31} - 30 q^{32} - 44 q^{33} - 4 q^{34} - 26 q^{35} + 32 q^{36} + 64 q^{37} - 75 q^{38} + 2 q^{39} - 5 q^{40} - 85 q^{41} - 13 q^{42} + 16 q^{43} - 66 q^{44} - 77 q^{45} - 100 q^{47} - 15 q^{48} + 64 q^{49} - 10 q^{50} - 55 q^{51} - 21 q^{52} - 23 q^{53} - 25 q^{54} - 19 q^{55} - 15 q^{56} + 7 q^{57} - 40 q^{58} - 125 q^{59} + 67 q^{60} - 17 q^{61} + 5 q^{62} + 56 q^{63} + 19 q^{64} - 38 q^{65} - 11 q^{66} - 33 q^{67} - 47 q^{68} - 52 q^{69} - 14 q^{70} - 129 q^{71} - 42 q^{72} - 37 q^{73} - 5 q^{74} - 108 q^{75} - 33 q^{76} - 37 q^{77} + 13 q^{78} - 14 q^{79} - 90 q^{80} + 56 q^{81} - 40 q^{82} - 114 q^{83} - 27 q^{84} + 3 q^{85} - 26 q^{86} + 7 q^{87} - 11 q^{88} - 72 q^{89} - 21 q^{90} - 18 q^{91} + 6 q^{92} + 18 q^{93} + q^{94} - 80 q^{95} - 26 q^{96} + q^{97} - 5 q^{98} - 82 q^{99}+O(q^{100}) \) 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 −2.78373 −1.87011 5.74916 1.28741 5.20588 1.00000 −10.4367 0.497300 −3.58380
1.2 −2.73543 2.30900 5.48259 −0.479374 −6.31610 1.00000 −9.52639 2.33146 1.31130
1.3 −2.60868 1.74395 4.80524 3.41549 −4.54942 1.00000 −7.31797 0.0413660 −8.90994
1.4 −2.55819 −1.74755 4.54434 −3.94326 4.47057 1.00000 −6.50890 0.0539426 10.0876
1.5 −2.54725 −0.119258 4.48849 −2.50621 0.303779 1.00000 −6.33880 −2.98578 6.38394
1.6 −2.47744 −3.01159 4.13771 −1.82686 7.46104 1.00000 −5.29605 6.06970 4.52594
1.7 −2.36739 2.20020 3.60455 −3.91478 −5.20875 1.00000 −3.79861 1.84090 9.26783
1.8 −2.29578 1.37707 3.27061 1.05070 −3.16145 1.00000 −2.91703 −1.10368 −2.41218
1.9 −2.23247 0.196842 2.98394 −3.18984 −0.439445 1.00000 −2.19661 −2.96125 7.12122
1.10 −2.05832 −2.27198 2.23670 1.17054 4.67648 1.00000 −0.487203 2.16191 −2.40935
1.11 −1.98856 1.88562 1.95439 2.26240 −3.74968 1.00000 0.0906987 0.555562 −4.49892
1.12 −1.97375 0.623779 1.89568 −0.759767 −1.23118 1.00000 0.205897 −2.61090 1.49959
1.13 −1.82754 −3.16895 1.33992 3.82020 5.79139 1.00000 1.20633 7.04224 −6.98159
1.14 −1.82638 −2.11005 1.33567 1.69503 3.85376 1.00000 1.21333 1.45233 −3.09578
1.15 −1.77753 3.13869 1.15960 −1.45610 −5.57910 1.00000 1.49384 6.85138 2.58826
1.16 −1.75707 −0.736428 1.08730 1.40549 1.29396 1.00000 1.60368 −2.45767 −2.46955
1.17 −1.74890 −3.08410 1.05865 −3.45153 5.39379 1.00000 1.64633 6.51170 6.03637
1.18 −1.65910 2.86279 0.752617 −1.19236 −4.74966 1.00000 2.06953 5.19558 1.97825
1.19 −1.63801 0.0795943 0.683081 2.69489 −0.130376 1.00000 2.15713 −2.99366 −4.41426
1.20 −1.50497 −2.68721 0.264943 −2.50384 4.04418 1.00000 2.61121 4.22109 3.76821
See all 64 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.64
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.b ✓ 64
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8029.2.a.b ✓ 64 1.a even 1 1 trivial