Properties

Label 6018.2.a.f
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

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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: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} - q^{6} - 2q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} + q^{4} - q^{6} - 2q^{7} + q^{8} + q^{9} - 2q^{11} - q^{12} - 2q^{13} - 2q^{14} + q^{16} + q^{17} + q^{18} + 4q^{19} + 2q^{21} - 2q^{22} + 4q^{23} - q^{24} - 5q^{25} - 2q^{26} - q^{27} - 2q^{28} + 4q^{29} + q^{32} + 2q^{33} + q^{34} + q^{36} - 2q^{37} + 4q^{38} + 2q^{39} - 2q^{41} + 2q^{42} + 8q^{43} - 2q^{44} + 4q^{46} - 8q^{47} - q^{48} - 3q^{49} - 5q^{50} - q^{51} - 2q^{52} - 6q^{53} - q^{54} - 2q^{56} - 4q^{57} + 4q^{58} - q^{59} + 6q^{61} - 2q^{63} + q^{64} + 2q^{66} - 4q^{67} + q^{68} - 4q^{69} + 2q^{71} + q^{72} + 8q^{73} - 2q^{74} + 5q^{75} + 4q^{76} + 4q^{77} + 2q^{78} - 14q^{79} + q^{81} - 2q^{82} - 12q^{83} + 2q^{84} + 8q^{86} - 4q^{87} - 2q^{88} - 10q^{89} + 4q^{91} + 4q^{92} - 8q^{94} - q^{96} + 8q^{97} - 3q^{98} - 2q^{99} + O(q^{100}) \)

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 0 −1.00000 −2.00000 1.00000 1.00000 0
\(n\): 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
\(2\) \(-1\)
\(3\) \(1\)
\(17\) \(-1\)
\(59\) \(1\)

Hecke kernels

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

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