Properties

Label 4018.2.a.e
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 574)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} - 2q^{9} + O(q^{10}) \) \( q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{8} - 2q^{9} + q^{10} + q^{11} - q^{12} - 2q^{13} + q^{15} + q^{16} + 2q^{18} + 3q^{19} - q^{20} - q^{22} - 4q^{23} + q^{24} - 4q^{25} + 2q^{26} + 5q^{27} + 8q^{29} - q^{30} + 10q^{31} - q^{32} - q^{33} - 2q^{36} - 2q^{37} - 3q^{38} + 2q^{39} + q^{40} - q^{41} - 4q^{43} + q^{44} + 2q^{45} + 4q^{46} + 8q^{47} - q^{48} + 4q^{50} - 2q^{52} - 2q^{53} - 5q^{54} - q^{55} - 3q^{57} - 8q^{58} - 10q^{59} + q^{60} + 5q^{61} - 10q^{62} + q^{64} + 2q^{65} + q^{66} - 8q^{67} + 4q^{69} - 9q^{71} + 2q^{72} - 2q^{73} + 2q^{74} + 4q^{75} + 3q^{76} - 2q^{78} + 15q^{79} - q^{80} + q^{81} + q^{82} + 6q^{83} + 4q^{86} - 8q^{87} - q^{88} + 6q^{89} - 2q^{90} - 4q^{92} - 10q^{93} - 8q^{94} - 3q^{95} + q^{96} - 16q^{97} - 2q^{99} + O(q^{100}) \)

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 −1.00000 1.00000 −1.00000 1.00000 0 −1.00000 −2.00000 1.00000
\(n\): 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.e 1
7.b odd 2 1 4018.2.a.h 1
7.c even 3 2 574.2.e.b 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
574.2.e.b 2 7.c even 3 2
4018.2.a.e 1 1.a even 1 1 trivial
4018.2.a.h 1 7.b odd 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4018))\):

\( T_{3} + 1 \)
\( T_{5} + 1 \)
\( T_{11} - 1 \)