Properties

Label 8018.2.a.g
Level $8018$
Weight $2$
Character orbit 8018.a
Self dual yes
Analytic conductor $64.024$
Analytic rank $1$
Dimension $34$
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: \(34\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 34 q - 34 q^{2} - 6 q^{3} + 34 q^{4} + q^{5} + 6 q^{6} - 22 q^{7} - 34 q^{8} + 30 q^{9} - q^{10} + 7 q^{11} - 6 q^{12} - 11 q^{13} + 22 q^{14} - 18 q^{15} + 34 q^{16} - 10 q^{17} - 30 q^{18} + 34 q^{19} + q^{20} + 14 q^{21} - 7 q^{22} - 30 q^{23} + 6 q^{24} + 11 q^{25} + 11 q^{26} - 21 q^{27} - 22 q^{28} + 12 q^{29} + 18 q^{30} - 13 q^{31} - 34 q^{32} - 4 q^{33} + 10 q^{34} - 16 q^{35} + 30 q^{36} - 46 q^{37} - 34 q^{38} - 36 q^{39} - q^{40} + 25 q^{41} - 14 q^{42} - 51 q^{43} + 7 q^{44} - 17 q^{45} + 30 q^{46} - 20 q^{47} - 6 q^{48} - 2 q^{49} - 11 q^{50} + 4 q^{51} - 11 q^{52} - 7 q^{53} + 21 q^{54} - 39 q^{55} + 22 q^{56} - 6 q^{57} - 12 q^{58} + 19 q^{59} - 18 q^{60} - 26 q^{61} + 13 q^{62} - 57 q^{63} + 34 q^{64} + 20 q^{65} + 4 q^{66} - 54 q^{67} - 10 q^{68} + 16 q^{70} + 9 q^{71} - 30 q^{72} - 57 q^{73} + 46 q^{74} + 26 q^{75} + 34 q^{76} + 2 q^{77} + 36 q^{78} - 7 q^{79} + q^{80} + 22 q^{81} - 25 q^{82} - 15 q^{83} + 14 q^{84} - 30 q^{85} + 51 q^{86} - 37 q^{87} - 7 q^{88} + 78 q^{89} + 17 q^{90} - 31 q^{91} - 30 q^{92} - 43 q^{93} + 20 q^{94} + q^{95} + 6 q^{96} - 38 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 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 −3.32805 1.00000 2.33043 3.32805 −1.71896 −1.00000 8.07595 −2.33043
1.2 −1.00000 −3.23421 1.00000 −1.01489 3.23421 2.27890 −1.00000 7.46011 1.01489
1.3 −1.00000 −3.00067 1.00000 −2.58515 3.00067 −5.14244 −1.00000 6.00401 2.58515
1.4 −1.00000 −2.69123 1.00000 2.65985 2.69123 −4.28568 −1.00000 4.24273 −2.65985
1.5 −1.00000 −2.58591 1.00000 −1.96812 2.58591 −0.600261 −1.00000 3.68694 1.96812
1.6 −1.00000 −2.57203 1.00000 3.90529 2.57203 −2.74849 −1.00000 3.61534 −3.90529
1.7 −1.00000 −2.37210 1.00000 −2.30761 2.37210 0.129234 −1.00000 2.62686 2.30761
1.8 −1.00000 −2.35248 1.00000 0.260869 2.35248 1.92119 −1.00000 2.53416 −0.260869
1.9 −1.00000 −1.88003 1.00000 1.30460 1.88003 −0.890859 −1.00000 0.534497 −1.30460
1.10 −1.00000 −1.50410 1.00000 0.693241 1.50410 2.70952 −1.00000 −0.737675 −0.693241
1.11 −1.00000 −1.36628 1.00000 2.24574 1.36628 3.44497 −1.00000 −1.13329 −2.24574
1.12 −1.00000 −1.32663 1.00000 −0.835058 1.32663 −1.21991 −1.00000 −1.24006 0.835058
1.13 −1.00000 −1.30982 1.00000 1.77709 1.30982 −3.58679 −1.00000 −1.28436 −1.77709
1.14 −1.00000 −1.00694 1.00000 −1.74347 1.00694 −4.04026 −1.00000 −1.98607 1.74347
1.15 −1.00000 −0.597156 1.00000 −2.37023 0.597156 1.41575 −1.00000 −2.64341 2.37023
1.16 −1.00000 −0.562142 1.00000 1.56640 0.562142 3.17308 −1.00000 −2.68400 −1.56640
1.17 −1.00000 −0.129854 1.00000 1.90646 0.129854 −0.0260326 −1.00000 −2.98314 −1.90646
1.18 −1.00000 0.0912120 1.00000 −2.07635 −0.0912120 −4.23935 −1.00000 −2.99168 2.07635
1.19 −1.00000 0.129131 1.00000 −3.52572 −0.129131 −2.82586 −1.00000 −2.98333 3.52572
1.20 −1.00000 0.234828 1.00000 −3.98534 −0.234828 1.98646 −1.00000 −2.94486 3.98534
See all 34 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.34
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.g 34
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8018.2.a.g 34 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{34} + 6 T_{3}^{33} - 48 T_{3}^{32} - 341 T_{3}^{31} + 932 T_{3}^{30} + 8611 T_{3}^{29} - 8495 T_{3}^{28} - 127477 T_{3}^{27} + 15030 T_{3}^{26} + 1228818 T_{3}^{25} + 493723 T_{3}^{24} - 8098990 T_{3}^{23} + \cdots - 800 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\). Copy content Toggle raw display