Properties

Label 6018.2.a.b
Level 6018
Weight 2
Character orbit 6018.a
Self dual yes
Analytic conductor 48.054
Analytic rank 1
Dimension 1
CM no
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6018.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(48.0539719364\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} - 2q^{5} + q^{6} + 2q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - q^{3} + q^{4} - 2q^{5} + q^{6} + 2q^{7} - q^{8} + q^{9} + 2q^{10} + 4q^{11} - q^{12} - 4q^{13} - 2q^{14} + 2q^{15} + q^{16} - q^{17} - q^{18} + 4q^{19} - 2q^{20} - 2q^{21} - 4q^{22} - 2q^{23} + q^{24} - q^{25} + 4q^{26} - q^{27} + 2q^{28} + 6q^{29} - 2q^{30} - 4q^{31} - q^{32} - 4q^{33} + q^{34} - 4q^{35} + q^{36} - 10q^{37} - 4q^{38} + 4q^{39} + 2q^{40} + 6q^{41} + 2q^{42} + 4q^{43} + 4q^{44} - 2q^{45} + 2q^{46} - q^{48} - 3q^{49} + q^{50} + q^{51} - 4q^{52} - 8q^{53} + q^{54} - 8q^{55} - 2q^{56} - 4q^{57} - 6q^{58} - q^{59} + 2q^{60} - 10q^{61} + 4q^{62} + 2q^{63} + q^{64} + 8q^{65} + 4q^{66} + 4q^{67} - q^{68} + 2q^{69} + 4q^{70} + 12q^{71} - q^{72} - 2q^{73} + 10q^{74} + q^{75} + 4q^{76} + 8q^{77} - 4q^{78} - 2q^{79} - 2q^{80} + q^{81} - 6q^{82} + 12q^{83} - 2q^{84} + 2q^{85} - 4q^{86} - 6q^{87} - 4q^{88} + 10q^{89} + 2q^{90} - 8q^{91} - 2q^{92} + 4q^{93} - 8q^{95} + q^{96} - 6q^{97} + 3q^{98} + 4q^{99} + O(q^{100}) \)

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 −2.00000 1.00000 2.00000 −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 6018.2.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6018.2.a.b 1 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(1\)
\(17\) \(1\)
\(59\) \(1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6018))\):

\( T_{5} + 2 \)
\( T_{7} - 2 \)