Properties

Label 6027.2.a.a
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

\(f(q)\) \(=\) \( q - 2q^{2} - q^{3} + 2q^{4} + 4q^{5} + 2q^{6} + q^{9} + O(q^{10}) \) \( q - 2q^{2} - q^{3} + 2q^{4} + 4q^{5} + 2q^{6} + q^{9} - 8q^{10} - 3q^{11} - 2q^{12} + 6q^{13} - 4q^{15} - 4q^{16} - 3q^{17} - 2q^{18} + 8q^{20} + 6q^{22} - 6q^{23} + 11q^{25} - 12q^{26} - q^{27} + 5q^{29} + 8q^{30} - 7q^{31} + 8q^{32} + 3q^{33} + 6q^{34} + 2q^{36} - 7q^{37} - 6q^{39} - q^{41} - q^{43} - 6q^{44} + 4q^{45} + 12q^{46} - 3q^{47} + 4q^{48} - 22q^{50} + 3q^{51} + 12q^{52} - 6q^{53} + 2q^{54} - 12q^{55} - 10q^{58} - 8q^{60} + 3q^{61} + 14q^{62} - 8q^{64} + 24q^{65} - 6q^{66} - 2q^{67} - 6q^{68} + 6q^{69} - 3q^{71} + 11q^{73} + 14q^{74} - 11q^{75} + 12q^{78} + 10q^{79} - 16q^{80} + q^{81} + 2q^{82} + 16q^{83} - 12q^{85} + 2q^{86} - 5q^{87} + 10q^{89} - 8q^{90} - 12q^{92} + 7q^{93} + 6q^{94} - 8q^{96} + 12q^{97} - 3q^{99} + O(q^{100}) \)

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
−2.00000 −1.00000 2.00000 4.00000 2.00000 0 0 1.00000 −8.00000
\(n\): 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6027))\):

\( T_{2} + 2 \)
\( T_{5} - 4 \)
\( T_{13} - 6 \)