Properties

Label 8018.2.a.d
Level $8018$
Weight $2$
Character orbit 8018.a
Self dual yes
Analytic conductor $64.024$
Analytic rank $1$
Dimension $30$
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: \(1\)
Dimension: \(30\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 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 −3.23056 1.00000 −3.65226 −3.23056 2.39039 1.00000 7.43653 −3.65226
1.2 1.00000 −3.09428 1.00000 2.68879 −3.09428 2.69798 1.00000 6.57455 2.68879
1.3 1.00000 −2.74076 1.00000 0.116951 −2.74076 −0.997196 1.00000 4.51179 0.116951
1.4 1.00000 −2.56870 1.00000 −1.11955 −2.56870 −1.44974 1.00000 3.59821 −1.11955
1.5 1.00000 −2.47683 1.00000 −0.567392 −2.47683 −4.82108 1.00000 3.13468 −0.567392
1.6 1.00000 −2.43818 1.00000 3.21483 −2.43818 −0.555600 1.00000 2.94471 3.21483
1.7 1.00000 −2.39570 1.00000 −3.46674 −2.39570 −3.11450 1.00000 2.73936 −3.46674
1.8 1.00000 −2.02842 1.00000 2.47134 −2.02842 1.41486 1.00000 1.11447 2.47134
1.9 1.00000 −1.51420 1.00000 −2.91196 −1.51420 −3.75064 1.00000 −0.707195 −2.91196
1.10 1.00000 −1.46114 1.00000 1.82408 −1.46114 −2.77663 1.00000 −0.865063 1.82408
1.11 1.00000 −1.44219 1.00000 −1.29569 −1.44219 1.46621 1.00000 −0.920075 −1.29569
1.12 1.00000 −1.14046 1.00000 1.90163 −1.14046 2.39414 1.00000 −1.69934 1.90163
1.13 1.00000 −0.894762 1.00000 −0.0669598 −0.894762 1.42997 1.00000 −2.19940 −0.0669598
1.14 1.00000 −0.851234 1.00000 −2.73591 −0.851234 0.590237 1.00000 −2.27540 −2.73591
1.15 1.00000 −0.785531 1.00000 −1.33472 −0.785531 4.52537 1.00000 −2.38294 −1.33472
1.16 1.00000 −0.219326 1.00000 2.27443 −0.219326 −3.32577 1.00000 −2.95190 2.27443
1.17 1.00000 0.180143 1.00000 0.229721 0.180143 −1.11361 1.00000 −2.96755 0.229721
1.18 1.00000 0.460726 1.00000 0.645126 0.460726 1.69833 1.00000 −2.78773 0.645126
1.19 1.00000 0.677734 1.00000 −4.37664 0.677734 −1.03965 1.00000 −2.54068 −4.37664
1.20 1.00000 0.846820 1.00000 2.51574 0.846820 −3.73115 1.00000 −2.28290 2.51574
See all 30 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.30
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.d 30
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8018.2.a.d 30 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{30} + 10 T_{3}^{29} - 301 T_{3}^{27} - 658 T_{3}^{26} + 3693 T_{3}^{25} + 12977 T_{3}^{24} - 22931 T_{3}^{23} - 124502 T_{3}^{22} + 63982 T_{3}^{21} + 728897 T_{3}^{20} + 63566 T_{3}^{19} - 2834921 T_{3}^{18} + \cdots + 5806 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\). Copy content Toggle raw display