Properties

Label 4018.2.a.o
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

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

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 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.o 1
7.b odd 2 1 574.2.a.i 1
21.c even 2 1 5166.2.a.h 1
28.d even 2 1 4592.2.a.i 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
574.2.a.i 1 7.b odd 2 1
4018.2.a.o 1 1.a even 1 1 trivial
4592.2.a.i 1 28.d even 2 1
5166.2.a.h 1 21.c 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4018))\):

\( T_{3} - 1 \)
\( T_{5} + 1 \)
\( T_{11} - 2 \)