Properties

Label 6018.2.a.a
Level 6018
Weight 2
Character orbit 6018.a
Self dual yes
Analytic conductor 48.054
Analytic rank 2
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: \(2\)
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

\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} - 4q^{5} + q^{6} - 2q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - q^{3} + q^{4} - 4q^{5} + q^{6} - 2q^{7} - q^{8} + q^{9} + 4q^{10} - 2q^{11} - q^{12} + 2q^{13} + 2q^{14} + 4q^{15} + q^{16} + q^{17} - q^{18} - 4q^{19} - 4q^{20} + 2q^{21} + 2q^{22} - 8q^{23} + q^{24} + 11q^{25} - 2q^{26} - q^{27} - 2q^{28} - 4q^{30} - 4q^{31} - q^{32} + 2q^{33} - q^{34} + 8q^{35} + q^{36} - 2q^{37} + 4q^{38} - 2q^{39} + 4q^{40} - 10q^{41} - 2q^{42} + 4q^{43} - 2q^{44} - 4q^{45} + 8q^{46} - 8q^{47} - q^{48} - 3q^{49} - 11q^{50} - q^{51} + 2q^{52} - 2q^{53} + q^{54} + 8q^{55} + 2q^{56} + 4q^{57} - q^{59} + 4q^{60} - 10q^{61} + 4q^{62} - 2q^{63} + q^{64} - 8q^{65} - 2q^{66} + 8q^{67} + q^{68} + 8q^{69} - 8q^{70} + 6q^{71} - q^{72} - 16q^{73} + 2q^{74} - 11q^{75} - 4q^{76} + 4q^{77} + 2q^{78} + 10q^{79} - 4q^{80} + q^{81} + 10q^{82} - 12q^{83} + 2q^{84} - 4q^{85} - 4q^{86} + 2q^{88} - 14q^{89} + 4q^{90} - 4q^{91} - 8q^{92} + 4q^{93} + 8q^{94} + 16q^{95} + q^{96} - 16q^{97} + 3q^{98} - 2q^{99} + O(q^{100}) \)

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 −4.00000 1.00000 −2.00000 −1.00000 1.00000 4.00000
\(n\): 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.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6018.2.a.a 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6018))\):

\( T_{5} + 4 \)
\( T_{7} + 2 \)