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Properties

Label 4029.2.a.i
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.

\(\operatorname{Tr}(f)(q) = \) \( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9} + 19 q^{10} + 19 q^{11} - 26 q^{12} + 4 q^{13} + 15 q^{14} + 2 q^{15} + 32 q^{16} + 25 q^{17} - 2 q^{18} + 29 q^{19} - 8 q^{20} - 12 q^{21} + 23 q^{22} + 6 q^{23} + 15 q^{25} - 8 q^{26} - 25 q^{27} + 23 q^{28} + 11 q^{29} - 19 q^{30} + 38 q^{31} - 27 q^{32} - 19 q^{33} - 2 q^{34} + 20 q^{35} + 26 q^{36} + 8 q^{37} - 25 q^{38} - 4 q^{39} + 48 q^{40} + 24 q^{41} - 15 q^{42} + 11 q^{43} + 6 q^{44} - 2 q^{45} + 25 q^{46} + 23 q^{47} - 32 q^{48} + 21 q^{49} - 21 q^{50} - 25 q^{51} + 31 q^{52} - 16 q^{53} + 2 q^{54} - 11 q^{55} + 18 q^{56} - 29 q^{57} - 5 q^{58} + 27 q^{59} + 8 q^{60} + 40 q^{61} - 34 q^{62} + 12 q^{63} + 46 q^{64} - 19 q^{65} - 23 q^{66} + 24 q^{67} + 26 q^{68} - 6 q^{69} + 17 q^{70} + 19 q^{71} + 13 q^{73} - 56 q^{74} - 15 q^{75} + 21 q^{76} - 30 q^{77} + 8 q^{78} - 25 q^{79} - 40 q^{80} + 25 q^{81} + 61 q^{82} + q^{83} - 23 q^{84} - 2 q^{85} + 62 q^{86} - 11 q^{87} - q^{88} - 10 q^{89} + 19 q^{90} + 50 q^{91} + 18 q^{92} - 38 q^{93} + 15 q^{94} + 14 q^{95} + 27 q^{96} + 19 q^{97} - 23 q^{98} + 19 q^{99}+O(q^{100}) \) 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 −2.74441 −1.00000 5.53180 1.03743 2.74441 3.45867 −9.69270 1.00000 −2.84714
1.2 −2.73699 −1.00000 5.49111 −3.81698 2.73699 −1.31322 −9.55513 1.00000 10.4470
1.3 −2.33071 −1.00000 3.43222 −2.50795 2.33071 −3.36649 −3.33810 1.00000 5.84531
1.4 −2.24485 −1.00000 3.03936 −1.59596 2.24485 3.55304 −2.33321 1.00000 3.58269
1.5 −1.94224 −1.00000 1.77230 1.77354 1.94224 −4.05542 0.442253 1.00000 −3.44464
1.6 −1.76780 −1.00000 1.12513 2.69545 1.76780 −0.714180 1.54660 1.00000 −4.76502
1.7 −1.65426 −1.00000 0.736566 1.27876 1.65426 3.55385 2.09004 1.00000 −2.11539
1.8 −1.40882 −1.00000 −0.0152236 −1.73169 1.40882 −3.56707 2.83909 1.00000 2.43964
1.9 −1.11147 −1.00000 −0.764631 −3.15121 1.11147 3.42561 3.07281 1.00000 3.50248
1.10 −0.756348 −1.00000 −1.42794 1.91333 0.756348 −1.89190 2.59271 1.00000 −1.44714
1.11 −0.693247 −1.00000 −1.51941 3.35677 0.693247 3.59459 2.43982 1.00000 −2.32707
1.12 −0.495377 −1.00000 −1.75460 −3.92669 0.495377 0.792012 1.85994 1.00000 1.94519
1.13 −0.141417 −1.00000 −1.98000 0.465802 0.141417 −1.58651 0.562841 1.00000 −0.0658725
1.14 −0.0249015 −1.00000 −1.99938 −2.90996 0.0249015 1.03650 0.0995904 1.00000 0.0724622
1.15 0.309286 −1.00000 −1.90434 −1.20431 −0.309286 2.27357 −1.20756 1.00000 −0.372476
1.16 0.454785 −1.00000 −1.79317 2.38795 −0.454785 0.109769 −1.72508 1.00000 1.08600
1.17 0.813229 −1.00000 −1.33866 1.02037 −0.813229 −1.92081 −2.71509 1.00000 0.829792
1.18 1.57851 −1.00000 0.491696 3.59209 −1.57851 3.03695 −2.38087 1.00000 5.67016
1.19 1.57938 −1.00000 0.494430 −1.92798 −1.57938 −2.95110 −2.37786 1.00000 −3.04500
1.20 1.74670 −1.00000 1.05095 −2.47902 −1.74670 4.46118 −1.65770 1.00000 −4.33009
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.i ✓ 25
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4029.2.a.i ✓ 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4029))\):

\( T_{2}^{25} + 2 T_{2}^{24} - 36 T_{2}^{23} - 72 T_{2}^{22} + 555 T_{2}^{21} + 1117 T_{2}^{20} - 4787 T_{2}^{19} + \cdots - 10 \) Copy content Toggle raw display
\( T_{5}^{25} + 2 T_{5}^{24} - 68 T_{5}^{23} - 124 T_{5}^{22} + 2020 T_{5}^{21} + 3336 T_{5}^{20} + \cdots - 8674443 \) Copy content Toggle raw display