Properties

Label 6027.2.a.f
Level 6027
Weight 2
Character orbit 6027.a
Self dual Yes
Analytic conductor 48.126
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
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

\(f(q)\) \(=\) \( q + q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - 3q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - 3q^{8} + q^{9} + q^{10} - 6q^{11} + q^{12} - 3q^{13} - q^{15} - q^{16} + 6q^{17} + q^{18} - 6q^{19} - q^{20} - 6q^{22} - 9q^{23} + 3q^{24} - 4q^{25} - 3q^{26} - q^{27} + 5q^{29} - q^{30} + 8q^{31} + 5q^{32} + 6q^{33} + 6q^{34} - q^{36} - 7q^{37} - 6q^{38} + 3q^{39} - 3q^{40} - q^{41} + 2q^{43} + 6q^{44} + q^{45} - 9q^{46} - 3q^{47} + q^{48} - 4q^{50} - 6q^{51} + 3q^{52} + 9q^{53} - q^{54} - 6q^{55} + 6q^{57} + 5q^{58} + 12q^{59} + q^{60} - 6q^{61} + 8q^{62} + 7q^{64} - 3q^{65} + 6q^{66} + 13q^{67} - 6q^{68} + 9q^{69} - 6q^{71} - 3q^{72} - 4q^{73} - 7q^{74} + 4q^{75} + 6q^{76} + 3q^{78} - 11q^{79} - q^{80} + q^{81} - q^{82} - 2q^{83} + 6q^{85} + 2q^{86} - 5q^{87} + 18q^{88} + 4q^{89} + q^{90} + 9q^{92} - 8q^{93} - 3q^{94} - 6q^{95} - 5q^{96} + 9q^{97} - 6q^{99} + O(q^{100}) \)

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 1.00000 −1.00000 0 −3.00000 1.00000 1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(7\) \(-1\)
\(41\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6027))\):

\( T_{2} - 1 \)
\( T_{5} - 1 \)
\( T_{13} + 3 \)