Properties

Label 8018.2.a.j
Level $8018$
Weight $2$
Character orbit 8018.a
Self dual yes
Analytic conductor $64.024$
Analytic rank $0$
Dimension $47$
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] = [8018,2,Mod(1,8018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8018, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("8018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8018.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: \(64.0240523407\)
Analytic rank: \(0\)
Dimension: \(47\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 1.00000 −3.22214 1.00000 3.63661 −3.22214 −0.166372 1.00000 7.38220 3.63661
1.2 1.00000 −3.13813 1.00000 2.17673 −3.13813 2.94096 1.00000 6.84787 2.17673
1.3 1.00000 −3.07943 1.00000 −3.30634 −3.07943 −2.62160 1.00000 6.48290 −3.30634
1.4 1.00000 −2.90959 1.00000 −4.15278 −2.90959 3.02073 1.00000 5.46571 −4.15278
1.5 1.00000 −2.83191 1.00000 1.28371 −2.83191 −4.11947 1.00000 5.01973 1.28371
1.6 1.00000 −2.78985 1.00000 −2.51493 −2.78985 −0.381461 1.00000 4.78329 −2.51493
1.7 1.00000 −2.41559 1.00000 0.828405 −2.41559 0.635145 1.00000 2.83509 0.828405
1.8 1.00000 −2.28341 1.00000 4.33431 −2.28341 −0.955796 1.00000 2.21398 4.33431
1.9 1.00000 −2.19254 1.00000 1.33631 −2.19254 −4.99100 1.00000 1.80723 1.33631
1.10 1.00000 −2.00763 1.00000 −1.79399 −2.00763 −2.43862 1.00000 1.03060 −1.79399
1.11 1.00000 −1.99735 1.00000 −0.291796 −1.99735 −0.492820 1.00000 0.989407 −0.291796
1.12 1.00000 −1.51480 1.00000 −1.33044 −1.51480 −3.41282 1.00000 −0.705394 −1.33044
1.13 1.00000 −1.46195 1.00000 2.14418 −1.46195 2.84565 1.00000 −0.862709 2.14418
1.14 1.00000 −1.39823 1.00000 0.539425 −1.39823 5.05784 1.00000 −1.04494 0.539425
1.15 1.00000 −1.14813 1.00000 2.89240 −1.14813 3.60462 1.00000 −1.68179 2.89240
1.16 1.00000 −1.10999 1.00000 3.90024 −1.10999 −4.77719 1.00000 −1.76791 3.90024
1.17 1.00000 −1.03614 1.00000 0.118794 −1.03614 2.13406 1.00000 −1.92642 0.118794
1.18 1.00000 −0.833135 1.00000 −3.18557 −0.833135 0.455061 1.00000 −2.30589 −3.18557
1.19 1.00000 −0.764189 1.00000 −0.445775 −0.764189 −0.938446 1.00000 −2.41602 −0.445775
1.20 1.00000 −0.316697 1.00000 −0.633871 −0.316697 1.30218 1.00000 −2.89970 −0.633871
See all 47 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.47
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(19\) \(1\)
\(211\) \(1\)

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 8018.2.a.j 47
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8018.2.a.j 47 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{47} - 10 T_{3}^{46} - 55 T_{3}^{45} + 849 T_{3}^{44} + 625 T_{3}^{43} - 32814 T_{3}^{42} + 32335 T_{3}^{41} + 762895 T_{3}^{40} - 1526765 T_{3}^{39} - 11859030 T_{3}^{38} + 33371501 T_{3}^{37} + \cdots - 2063488 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\). Copy content Toggle raw display