Properties

Label 4018.2.a.l
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

\(f(q)\) \(=\) \( q + q^{2} - 2q^{3} + q^{4} + 2q^{5} - 2q^{6} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - 2q^{3} + q^{4} + 2q^{5} - 2q^{6} + q^{8} + q^{9} + 2q^{10} - 4q^{11} - 2q^{12} - q^{13} - 4q^{15} + q^{16} + q^{18} + 6q^{19} + 2q^{20} - 4q^{22} - 2q^{23} - 2q^{24} - q^{25} - q^{26} + 4q^{27} - 5q^{29} - 4q^{30} - 4q^{31} + q^{32} + 8q^{33} + q^{36} - 2q^{37} + 6q^{38} + 2q^{39} + 2q^{40} - q^{41} - q^{43} - 4q^{44} + 2q^{45} - 2q^{46} + 8q^{47} - 2q^{48} - q^{50} - q^{52} - 10q^{53} + 4q^{54} - 8q^{55} - 12q^{57} - 5q^{58} - q^{59} - 4q^{60} - 14q^{61} - 4q^{62} + q^{64} - 2q^{65} + 8q^{66} + 10q^{67} + 4q^{69} - 15q^{71} + q^{72} - 7q^{73} - 2q^{74} + 2q^{75} + 6q^{76} + 2q^{78} + 2q^{80} - 11q^{81} - q^{82} - 9q^{83} - q^{86} + 10q^{87} - 4q^{88} + 2q^{90} - 2q^{92} + 8q^{93} + 8q^{94} + 12q^{95} - 2q^{96} + 4q^{97} - 4q^{99} + O(q^{100}) \)

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.l 1
7.b odd 2 1 4018.2.a.r 1
7.d odd 6 2 574.2.e.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
574.2.e.a 2 7.d odd 6 2
4018.2.a.l 1 1.a even 1 1 trivial
4018.2.a.r 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4018))\):

\( T_{3} + 2 \)
\( T_{5} - 2 \)
\( T_{11} + 4 \)