Properties

Label 6018.2.a.d
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

Downloads

Learn more about

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

\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} - q^{6} + 5q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + q^{3} + q^{4} - q^{6} + 5q^{7} - q^{8} + q^{9} - 6q^{11} + q^{12} + 2q^{13} - 5q^{14} + q^{16} - q^{17} - q^{18} - q^{19} + 5q^{21} + 6q^{22} - 9q^{23} - q^{24} - 5q^{25} - 2q^{26} + q^{27} + 5q^{28} + 6q^{29} + 2q^{31} - q^{32} - 6q^{33} + q^{34} + q^{36} - 10q^{37} + q^{38} + 2q^{39} - 3q^{41} - 5q^{42} - 10q^{43} - 6q^{44} + 9q^{46} - 6q^{47} + q^{48} + 18q^{49} + 5q^{50} - q^{51} + 2q^{52} - 3q^{53} - q^{54} - 5q^{56} - q^{57} - 6q^{58} + q^{59} + 2q^{61} - 2q^{62} + 5q^{63} + q^{64} + 6q^{66} - 4q^{67} - q^{68} - 9q^{69} - 12q^{71} - q^{72} - 7q^{73} + 10q^{74} - 5q^{75} - q^{76} - 30q^{77} - 2q^{78} + 8q^{79} + q^{81} + 3q^{82} - 9q^{83} + 5q^{84} + 10q^{86} + 6q^{87} + 6q^{88} + 3q^{89} + 10q^{91} - 9q^{92} + 2q^{93} + 6q^{94} - q^{96} - 7q^{97} - 18q^{98} - 6q^{99} + O(q^{100}) \)

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 5.00000 −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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6018))\):

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