Properties

Label 4018.2.a.j
Level 4018
Weight 2
Character orbit 4018.a
Self dual yes
Analytic conductor 32.084
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4018 = 2 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4018.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0838915322\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 82)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + 2q^{3} + q^{4} + 2q^{5} - 2q^{6} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + 2q^{3} + q^{4} + 2q^{5} - 2q^{6} - q^{8} + q^{9} - 2q^{10} - 2q^{11} + 2q^{12} - 4q^{13} + 4q^{15} + q^{16} + 2q^{17} - q^{18} - 6q^{19} + 2q^{20} + 2q^{22} - 8q^{23} - 2q^{24} - q^{25} + 4q^{26} - 4q^{27} - 4q^{30} + 8q^{31} - q^{32} - 4q^{33} - 2q^{34} + q^{36} + 2q^{37} + 6q^{38} - 8q^{39} - 2q^{40} + q^{41} - 12q^{43} - 2q^{44} + 2q^{45} + 8q^{46} - 4q^{47} + 2q^{48} + q^{50} + 4q^{51} - 4q^{52} - 4q^{53} + 4q^{54} - 4q^{55} - 12q^{57} - 8q^{59} + 4q^{60} + 14q^{61} - 8q^{62} + q^{64} - 8q^{65} + 4q^{66} - 2q^{67} + 2q^{68} - 16q^{69} + 8q^{71} - q^{72} - 10q^{73} - 2q^{74} - 2q^{75} - 6q^{76} + 8q^{78} + 4q^{79} + 2q^{80} - 11q^{81} - q^{82} - 12q^{83} + 4q^{85} + 12q^{86} + 2q^{88} + 14q^{89} - 2q^{90} - 8q^{92} + 16q^{93} + 4q^{94} - 12q^{95} - 2q^{96} - 6q^{97} - 2q^{99} + O(q^{100}) \)

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.

Label \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
−1.00000 2.00000 1.00000 2.00000 −2.00000 0 −1.00000 1.00000 −2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

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 4018.2.a.j 1
7.b odd 2 1 82.2.a.a 1
21.c even 2 1 738.2.a.h 1
28.d even 2 1 656.2.a.c 1
35.c odd 2 1 2050.2.a.g 1
35.f even 4 2 2050.2.c.e 2
56.e even 2 1 2624.2.a.c 1
56.h odd 2 1 2624.2.a.g 1
77.b even 2 1 9922.2.a.c 1
84.h odd 2 1 5904.2.a.s 1
287.d odd 2 1 3362.2.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
82.2.a.a 1 7.b odd 2 1
656.2.a.c 1 28.d even 2 1
738.2.a.h 1 21.c even 2 1
2050.2.a.g 1 35.c odd 2 1
2050.2.c.e 2 35.f even 4 2
2624.2.a.c 1 56.e even 2 1
2624.2.a.g 1 56.h odd 2 1
3362.2.a.b 1 287.d odd 2 1
4018.2.a.j 1 1.a even 1 1 trivial
5904.2.a.s 1 84.h odd 2 1
9922.2.a.c 1 77.b even 2 1

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(7\) \(-1\)
\(41\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4018))\):

\( T_{3} - 2 \)
\( T_{5} - 2 \)
\( T_{11} + 2 \)