Properties

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

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} - 3q^{3} + q^{4} + q^{5} + 3q^{6} - q^{8} + 6q^{9} + O(q^{10}) \) \( q - q^{2} - 3q^{3} + q^{4} + q^{5} + 3q^{6} - q^{8} + 6q^{9} - q^{10} + 4q^{11} - 3q^{12} + 6q^{13} - 3q^{15} + q^{16} - 3q^{17} - 6q^{18} - 4q^{19} + q^{20} - 4q^{22} + 2q^{23} + 3q^{24} - 4q^{25} - 6q^{26} - 9q^{27} + q^{29} + 3q^{30} - 9q^{31} - q^{32} - 12q^{33} + 3q^{34} + 6q^{36} - 8q^{37} + 4q^{38} - 18q^{39} - q^{40} + q^{41} - 5q^{43} + 4q^{44} + 6q^{45} - 2q^{46} + 6q^{47} - 3q^{48} + 4q^{50} + 9q^{51} + 6q^{52} - 3q^{53} + 9q^{54} + 4q^{55} + 12q^{57} - q^{58} - 14q^{59} - 3q^{60} + 11q^{61} + 9q^{62} + q^{64} + 6q^{65} + 12q^{66} - 8q^{67} - 3q^{68} - 6q^{69} + 3q^{71} - 6q^{72} + 14q^{73} + 8q^{74} + 12q^{75} - 4q^{76} + 18q^{78} + 7q^{79} + q^{80} + 9q^{81} - q^{82} - 16q^{83} - 3q^{85} + 5q^{86} - 3q^{87} - 4q^{88} - 5q^{89} - 6q^{90} + 2q^{92} + 27q^{93} - 6q^{94} - 4q^{95} + 3q^{96} - q^{97} + 24q^{99} + O(q^{100}) \)

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 −3.00000 1.00000 1.00000 3.00000 0 −1.00000 6.00000 −1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Atkin-Lehner signs

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

Hecke kernels

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

\( T_{3} + 3 \)
\( T_{5} - 1 \)
\( T_{11} - 4 \)