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Properties

Label 4029.2.a.h
Level $4029$
Weight $2$
Character orbit 4029.a
Self dual yes
Analytic conductor $32.172$
Analytic rank $1$
Dimension $25$
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] = [4029,2,Mod(1,4029)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4029, 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("4029.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4029.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: \(32.1717269744\)
Analytic rank: \(1\)
Dimension: \(25\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 25 q - 7 q^{2} + 25 q^{3} + 21 q^{4} - 12 q^{5} - 7 q^{6} - 4 q^{7} - 21 q^{8} + 25 q^{9} - 9 q^{10} - 19 q^{11} + 21 q^{12} - 12 q^{13} - 15 q^{14} - 12 q^{15} + q^{16} - 25 q^{17} - 7 q^{18} - 35 q^{19} - 11 q^{20} - 4 q^{21} - 2 q^{22} - 16 q^{23} - 21 q^{24} + 19 q^{25} - 5 q^{26} + 25 q^{27} + 3 q^{28} - 37 q^{29} - 9 q^{30} - 28 q^{31} - 19 q^{32} - 19 q^{33} + 7 q^{34} - 42 q^{35} + 21 q^{36} + 8 q^{37} - 35 q^{38} - 12 q^{39} - 9 q^{40} - 34 q^{41} - 15 q^{42} - 19 q^{43} - 56 q^{44} - 12 q^{45} + q^{46} - 25 q^{47} + q^{48} + 25 q^{49} - 7 q^{50} - 25 q^{51} - 37 q^{52} - 44 q^{53} - 7 q^{54} - 11 q^{55} - 18 q^{56} - 35 q^{57} - 3 q^{58} - 47 q^{59} - 11 q^{60} - 28 q^{61} + 11 q^{62} - 4 q^{63} - 9 q^{64} - 63 q^{65} - 2 q^{66} - 28 q^{67} - 21 q^{68} - 16 q^{69} + 5 q^{70} - 27 q^{71} - 21 q^{72} - 21 q^{73} - 18 q^{74} + 19 q^{75} - 50 q^{76} - 58 q^{77} - 5 q^{78} + 25 q^{79} - 56 q^{80} + 25 q^{81} - 5 q^{82} - 61 q^{83} + 3 q^{84} + 12 q^{85} - 28 q^{86} - 37 q^{87} + 15 q^{88} - 34 q^{89} - 9 q^{90} - 30 q^{91} - 31 q^{92} - 28 q^{93} + q^{94} - 32 q^{95} - 19 q^{96} - 11 q^{97} - 66 q^{98} - 19 q^{99}+O(q^{100}) \) 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 −2.72160 1.00000 5.40711 −2.75991 −2.72160 0.631996 −9.27279 1.00000 7.51137
1.2 −2.56536 1.00000 4.58108 2.03955 −2.56536 3.97532 −6.62141 1.00000 −5.23220
1.3 −2.38168 1.00000 3.67240 4.36966 −2.38168 −4.18483 −3.98313 1.00000 −10.4071
1.4 −2.32685 1.00000 3.41424 −3.48051 −2.32685 3.88205 −3.29073 1.00000 8.09862
1.5 −2.14934 1.00000 2.61967 −2.01369 −2.14934 −1.06654 −1.33187 1.00000 4.32810
1.6 −2.03763 1.00000 2.15194 1.97362 −2.03763 1.01571 −0.309598 1.00000 −4.02151
1.7 −2.01259 1.00000 2.05052 −0.898800 −2.01259 −4.86016 −0.101684 1.00000 1.80892
1.8 −1.64354 1.00000 0.701226 −1.87389 −1.64354 4.02619 2.13459 1.00000 3.07982
1.9 −1.29135 1.00000 −0.332415 2.00535 −1.29135 −2.01131 3.01196 1.00000 −2.58960
1.10 −1.16862 1.00000 −0.634325 −0.405562 −1.16862 −1.60950 3.07853 1.00000 0.473948
1.11 −0.743888 1.00000 −1.44663 0.602376 −0.743888 4.42261 2.56391 1.00000 −0.448100
1.12 −0.691575 1.00000 −1.52172 1.10999 −0.691575 −0.538181 2.43554 1.00000 −0.767639
1.13 −0.319374 1.00000 −1.89800 −2.81066 −0.319374 −2.62902 1.24492 1.00000 0.897652
1.14 −0.107521 1.00000 −1.98844 −4.11054 −0.107521 −2.41834 0.428841 1.00000 0.441969
1.15 0.0993996 1.00000 −1.99012 1.12985 0.0993996 0.411227 −0.396616 1.00000 0.112306
1.16 0.384561 1.00000 −1.85211 −1.18123 0.384561 2.30830 −1.48137 1.00000 −0.454254
1.17 0.785597 1.00000 −1.38284 −0.680986 0.785597 0.961909 −2.65755 1.00000 −0.534981
1.18 1.22160 1.00000 −0.507691 −3.76998 1.22160 4.22641 −3.06340 1.00000 −4.60542
1.19 1.36573 1.00000 −0.134771 0.714593 1.36573 −2.88499 −2.91553 1.00000 0.975944
1.20 1.40291 1.00000 −0.0318502 3.36351 1.40291 −1.96099 −2.85050 1.00000 4.71869
See all 25 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.25
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(17\) \(1\)
\(79\) \(-1\)

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 4029.2.a.h ✓ 25
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4029.2.a.h ✓ 25 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4029))\):

\( T_{2}^{25} + 7 T_{2}^{24} - 11 T_{2}^{23} - 175 T_{2}^{22} - 107 T_{2}^{21} + 1835 T_{2}^{20} + \cdots - 30 \) Copy content Toggle raw display
\( T_{5}^{25} + 12 T_{5}^{24} - 526 T_{5}^{22} - 1532 T_{5}^{21} + 7916 T_{5}^{20} + 38952 T_{5}^{19} + \cdots - 670191 \) Copy content Toggle raw display