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Properties

Label 4029.2.a.j
Level $4029$
Weight $2$
Character orbit 4029.a
Self dual yes
Analytic conductor $32.172$
Analytic rank $0$
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: \(0\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9} + 13 q^{10} + 19 q^{11} + 26 q^{12} + 17 q^{14} + 6 q^{15} + 16 q^{16} - 25 q^{17} + 6 q^{18} + 25 q^{19} + 32 q^{20} + 4 q^{21} - 7 q^{22} + 8 q^{23} + 18 q^{24} + 15 q^{25} + 20 q^{26} + 25 q^{27} + 9 q^{28} + 21 q^{29} + 13 q^{30} + 4 q^{31} + 27 q^{32} + 19 q^{33} - 6 q^{34} + 50 q^{35} + 26 q^{36} - 8 q^{37} + 31 q^{38} + 52 q^{40} + 40 q^{41} + 17 q^{42} + 21 q^{43} + 34 q^{44} + 6 q^{45} + 29 q^{46} + 43 q^{47} + 16 q^{48} + 21 q^{49} + 13 q^{50} - 25 q^{51} + 3 q^{52} + 44 q^{53} + 6 q^{54} + 13 q^{55} + 38 q^{56} + 25 q^{57} - 5 q^{58} + 45 q^{59} + 32 q^{60} + 22 q^{61} + 4 q^{62} + 4 q^{63} + 26 q^{64} + 43 q^{65} - 7 q^{66} + 8 q^{67} - 26 q^{68} + 8 q^{69} + 29 q^{70} + 9 q^{71} + 18 q^{72} - 7 q^{73} + 18 q^{74} + 15 q^{75} + 33 q^{76} + 20 q^{77} + 20 q^{78} - 25 q^{79} + 42 q^{80} + 25 q^{81} - 43 q^{82} + 41 q^{83} + 9 q^{84} - 6 q^{85} - 12 q^{86} + 21 q^{87} - 43 q^{88} + 68 q^{89} + 13 q^{90} + 10 q^{91} + 2 q^{92} + 4 q^{93} - 17 q^{94} + 8 q^{95} + 27 q^{96} + 15 q^{97} + 11 q^{98} + 19 q^{99}+O(q^{100}) \) 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 −2.64938 1.00000 5.01922 0.160966 −2.64938 −0.166444 −7.99906 1.00000 −0.426461
1.2 −2.33976 1.00000 3.47445 −0.253256 −2.33976 −1.85897 −3.44986 1.00000 0.592558
1.3 −2.01628 1.00000 2.06539 1.36022 −2.01628 −1.99574 −0.131838 1.00000 −2.74259
1.4 −1.89235 1.00000 1.58099 −3.51419 −1.89235 −2.76756 0.792916 1.00000 6.65008
1.5 −1.73737 1.00000 1.01844 3.91288 −1.73737 2.21072 1.70533 1.00000 −6.79810
1.6 −1.71946 1.00000 0.956548 −0.401705 −1.71946 3.91285 1.79418 1.00000 0.690716
1.7 −1.19187 1.00000 −0.579444 −1.97485 −1.19187 1.20760 3.07436 1.00000 2.35376
1.8 −0.991328 1.00000 −1.01727 3.49390 −0.991328 −2.79439 2.99110 1.00000 −3.46360
1.9 −0.960337 1.00000 −1.07775 −2.82407 −0.960337 −0.386767 2.95568 1.00000 2.71206
1.10 −0.645538 1.00000 −1.58328 2.70107 −0.645538 4.18986 2.31314 1.00000 −1.74364
1.11 −0.517388 1.00000 −1.73231 −0.162302 −0.517388 −5.01323 1.93105 1.00000 0.0839730
1.12 0.367511 1.00000 −1.86494 −0.382809 0.367511 2.18053 −1.42041 1.00000 −0.140687
1.13 0.375442 1.00000 −1.85904 −2.43598 0.375442 3.04964 −1.44885 1.00000 −0.914570
1.14 0.777638 1.00000 −1.39528 1.77745 0.777638 0.717944 −2.64030 1.00000 1.38222
1.15 0.782307 1.00000 −1.38800 −1.22158 0.782307 −4.37722 −2.65045 1.00000 −0.955651
1.16 1.12130 1.00000 −0.742675 3.71073 1.12130 4.45947 −3.07538 1.00000 4.16086
1.17 1.24074 1.00000 −0.460556 −3.76050 1.24074 −4.20824 −3.05292 1.00000 −4.66581
1.18 1.54939 1.00000 0.400614 −2.39535 1.54939 1.82690 −2.47808 1.00000 −3.71134
1.19 1.88836 1.00000 1.56590 −1.95166 1.88836 −1.51083 −0.819741 1.00000 −3.68543
1.20 2.09012 1.00000 2.36860 3.44470 2.09012 0.589185 0.770426 1.00000 7.19983
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.j ✓ 25
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4029.2.a.j ✓ 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4029))\):

\( T_{2}^{25} - 6 T_{2}^{24} - 20 T_{2}^{23} + 178 T_{2}^{22} + 83 T_{2}^{21} - 2249 T_{2}^{20} + \cdots + 1820 \) Copy content Toggle raw display
\( T_{5}^{25} - 6 T_{5}^{24} - 52 T_{5}^{23} + 350 T_{5}^{22} + 1094 T_{5}^{21} - 8636 T_{5}^{20} + \cdots + 9459 \) Copy content Toggle raw display