↑

Properties

Label 8029.2.a.f
Level $8029$
Weight $2$
Character orbit 8029.a
Self dual yes
Analytic conductor $64.112$
Analytic rank $0$
Dimension $69$
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: \(0\)
Dimension: \(69\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 69 q + 8 q^{2} + 12 q^{3} + 72 q^{4} + 30 q^{5} + 15 q^{6} + 69 q^{7} + 24 q^{8} + 81 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 69 q + 8 q^{2} + 12 q^{3} + 72 q^{4} + 30 q^{5} + 15 q^{6} + 69 q^{7} + 24 q^{8} + 81 q^{9} + 14 q^{10} + 29 q^{11} + 23 q^{12} + 24 q^{13} + 8 q^{14} + 16 q^{15} + 74 q^{16} + 35 q^{17} + 7 q^{18} + 43 q^{19} + 65 q^{20} + 12 q^{21} + 12 q^{22} + 14 q^{23} + 45 q^{24} + 83 q^{25} + 13 q^{26} + 54 q^{27} + 72 q^{28} + 2 q^{29} + 22 q^{30} - 69 q^{31} + 51 q^{32} + 44 q^{33} + 6 q^{34} + 30 q^{35} + 107 q^{36} - 69 q^{37} + 37 q^{38} + 56 q^{39} + 23 q^{40} + 37 q^{41} + 15 q^{42} + 12 q^{43} + 50 q^{44} + 91 q^{45} + 28 q^{46} + 30 q^{47} + 65 q^{48} + 69 q^{49} + 81 q^{50} + 77 q^{51} + 69 q^{52} - 19 q^{53} + 45 q^{54} + 41 q^{55} + 24 q^{56} + 19 q^{57} - 34 q^{58} + 145 q^{59} + 23 q^{60} + 7 q^{61} - 8 q^{62} + 81 q^{63} + 94 q^{64} + 18 q^{65} + 57 q^{66} + 51 q^{67} + 113 q^{68} + 52 q^{69} + 14 q^{70} + 75 q^{71} + 27 q^{72} + 33 q^{73} - 8 q^{74} + 50 q^{75} + 121 q^{76} + 29 q^{77} - 99 q^{78} + 18 q^{79} + 142 q^{80} + 61 q^{81} - 2 q^{82} + 68 q^{83} + 23 q^{84} - 21 q^{85} + 20 q^{86} + 93 q^{87} - 5 q^{88} + 80 q^{89} - 29 q^{90} + 24 q^{91} + 24 q^{92} - 12 q^{93} - 9 q^{94} + 4 q^{95} + 40 q^{96} + 67 q^{97} + 8 q^{98} + 84 q^{99}+O(q^{100}) \) 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 −2.67565 1.91120 5.15909 2.59310 −5.11369 1.00000 −8.45261 0.652680 −6.93823
1.2 −2.61416 −1.74326 4.83381 3.93156 4.55715 1.00000 −7.40802 0.0389496 −10.2777
1.3 −2.60615 1.42811 4.79203 −0.233642 −3.72188 1.00000 −7.27646 −0.960493 0.608906
1.4 −2.60059 0.611656 4.76307 −1.34510 −1.59067 1.00000 −7.18561 −2.62588 3.49805
1.5 −2.52981 −3.20507 4.39992 −1.26852 8.10820 1.00000 −6.07133 7.27246 3.20912
1.6 −2.39748 −1.29627 3.74792 −0.588449 3.10779 1.00000 −4.19060 −1.31968 1.41080
1.7 −2.39526 3.45538 3.73727 1.09165 −8.27652 1.00000 −4.16120 8.93963 −2.61478
1.8 −2.37456 −2.31406 3.63853 3.34698 5.49486 1.00000 −3.89080 2.35485 −7.94760
1.9 −2.09043 −0.621125 2.36990 −0.355441 1.29842 1.00000 −0.773254 −2.61420 0.743024
1.10 −2.08278 2.57754 2.33797 −2.78870 −5.36845 1.00000 −0.703927 3.64370 5.80824
1.11 −2.06201 −1.74903 2.25190 −0.353831 3.60653 1.00000 −0.519419 0.0591143 0.729604
1.12 −1.88068 3.04102 1.53695 3.34677 −5.71917 1.00000 0.870856 6.24779 −6.29420
1.13 −1.74975 1.15866 1.06162 0.539752 −2.02735 1.00000 1.64194 −1.65752 −0.944429
1.14 −1.68688 −2.15991 0.845567 3.01913 3.64351 1.00000 1.94739 1.66521 −5.09291
1.15 −1.58632 0.873515 0.516407 0.00202918 −1.38567 1.00000 2.35345 −2.23697 −0.00321892
1.16 −1.57783 −0.881197 0.489533 −2.86021 1.39037 1.00000 2.38325 −2.22349 4.51291
1.17 −1.56024 2.35485 0.434342 3.18014 −3.67413 1.00000 2.44280 2.54532 −4.96177
1.18 −1.52231 −1.18145 0.317421 −3.73395 1.79853 1.00000 2.56140 −1.60417 5.68423
1.19 −1.44064 −2.18382 0.0754300 −2.57302 3.14609 1.00000 2.77260 1.76906 3.70678
1.20 −1.32008 1.26442 −0.257389 −2.82638 −1.66913 1.00000 2.97993 −1.40124 3.73105
See all 69 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.69
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.f ✓ 69
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8029.2.a.f ✓ 69 1.a even 1 1 trivial