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Properties

Label 4029.2.a.f
Level $4029$
Weight $2$
Character orbit 4029.a
Self dual yes
Analytic conductor $32.172$
Analytic rank $1$
Dimension $22$
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: \(22\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9} - 13 q^{10} - 23 q^{11} - 19 q^{12} - 18 q^{13} - 9 q^{14} - q^{15} + 21 q^{16} + 22 q^{17} + q^{18} - 30 q^{19} - 7 q^{20} + 15 q^{21} + 4 q^{22} - 3 q^{23} - 15 q^{24} + 19 q^{25} - 7 q^{26} - 22 q^{27} - 25 q^{28} - 7 q^{29} + 13 q^{30} - 10 q^{31} + 31 q^{32} + 23 q^{33} + q^{34} - 11 q^{35} + 19 q^{36} - q^{37} - 29 q^{38} + 18 q^{39} - 59 q^{40} + 9 q^{42} - 43 q^{43} - 80 q^{44} + q^{45} - 43 q^{46} + 2 q^{47} - 21 q^{48} + 43 q^{49} + 25 q^{50} - 22 q^{51} - 5 q^{52} - q^{53} - q^{54} - 19 q^{55} - 8 q^{56} + 30 q^{57} - 43 q^{58} - 28 q^{59} + 7 q^{60} - 29 q^{61} - 3 q^{62} - 15 q^{63} + 23 q^{64} + 19 q^{65} - 4 q^{66} - 16 q^{67} + 19 q^{68} + 3 q^{69} - 5 q^{70} - q^{71} + 15 q^{72} - 19 q^{73} - 24 q^{74} - 19 q^{75} - 72 q^{76} + 24 q^{77} + 7 q^{78} + 22 q^{79} - 82 q^{80} + 22 q^{81} - 81 q^{82} - 29 q^{83} + 25 q^{84} + q^{85} - 42 q^{86} + 7 q^{87} - 43 q^{88} - 28 q^{89} - 13 q^{90} - 96 q^{91} - 11 q^{92} + 10 q^{93} - 63 q^{94} - 23 q^{95} - 31 q^{96} - 51 q^{97} + 12 q^{98} - 23 q^{99}+O(q^{100}) \) 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 −2.46822 −1.00000 4.09210 0.833166 2.46822 −0.715489 −5.16375 1.00000 −2.05644
1.2 −2.41406 −1.00000 3.82770 1.38907 2.41406 −5.15713 −4.41218 1.00000 −3.35331
1.3 −2.30059 −1.00000 3.29272 −0.193972 2.30059 1.10356 −2.97403 1.00000 0.446250
1.4 −1.97908 −1.00000 1.91674 3.55725 1.97908 2.67617 0.164776 1.00000 −7.04007
1.5 −1.55293 −1.00000 0.411606 −3.25042 1.55293 1.50369 2.46667 1.00000 5.04769
1.6 −1.21952 −1.00000 −0.512778 −1.58706 1.21952 −3.41478 3.06438 1.00000 1.93545
1.7 −1.18480 −1.00000 −0.596253 −2.40127 1.18480 −0.655760 3.07604 1.00000 2.84502
1.8 −0.922410 −1.00000 −1.14916 −0.0437394 0.922410 4.58186 2.90482 1.00000 0.0403457
1.9 −0.891747 −1.00000 −1.20479 2.60961 0.891747 −3.10366 2.85786 1.00000 −2.32711
1.10 −0.821645 −1.00000 −1.32490 1.58661 0.821645 1.25319 2.73189 1.00000 −1.30363
1.11 −0.236594 −1.00000 −1.94402 3.94072 0.236594 −1.91925 0.933134 1.00000 −0.932353
1.12 0.220817 −1.00000 −1.95124 −3.79014 −0.220817 −3.98824 −0.872503 1.00000 −0.836928
1.13 0.736590 −1.00000 −1.45743 −2.90793 −0.736590 −3.09183 −2.54671 1.00000 −2.14196
1.14 0.795328 −1.00000 −1.36745 2.82245 −0.795328 −3.74228 −2.67823 1.00000 2.24477
1.15 0.799151 −1.00000 −1.36136 0.403932 −0.799151 1.36573 −2.68623 1.00000 0.322802
1.16 0.843162 −1.00000 −1.28908 −2.14706 −0.843162 4.16350 −2.77323 1.00000 −1.81032
1.17 1.73045 −1.00000 0.994457 2.73352 −1.73045 −2.97598 −1.74004 1.00000 4.73022
1.18 1.95682 −1.00000 1.82914 0.334746 −1.95682 4.67011 −0.334351 1.00000 0.655037
1.19 2.12169 −1.00000 2.50157 3.09428 −2.12169 −1.64576 1.06418 1.00000 6.56509
1.20 2.37194 −1.00000 3.62611 −0.369639 −2.37194 −3.46859 3.85703 1.00000 −0.876762
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.22
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.f ✓ 22
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4029.2.a.f ✓ 22 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4029))\):

\( T_{2}^{22} - T_{2}^{21} - 31 T_{2}^{20} + 25 T_{2}^{19} + 409 T_{2}^{18} - 251 T_{2}^{17} - 2996 T_{2}^{16} + \cdots - 106 \) Copy content Toggle raw display
\( T_{5}^{22} - T_{5}^{21} - 64 T_{5}^{20} + 62 T_{5}^{19} + 1723 T_{5}^{18} - 1617 T_{5}^{17} + \cdots - 1435 \) Copy content Toggle raw display