Properties

Label 6003.2.a.a
Level 6003
Weight 2
Character orbit 6003.a
Self dual Yes
Analytic conductor 47.934
Analytic rank 1
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9341963334\)
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

\(f(q)\) \(=\) \( q - 2q^{4} - 4q^{5} - 4q^{7} + O(q^{10}) \) \( q - 2q^{4} - 4q^{5} - 4q^{7} - 4q^{11} - 5q^{13} + 4q^{16} + 5q^{17} + 5q^{19} + 8q^{20} - q^{23} + 11q^{25} + 8q^{28} + q^{29} - 2q^{31} + 16q^{35} + 5q^{37} + 2q^{41} + q^{43} + 8q^{44} - 6q^{47} + 9q^{49} + 10q^{52} - 2q^{53} + 16q^{55} - 9q^{59} - 10q^{61} - 8q^{64} + 20q^{65} + 8q^{67} - 10q^{68} + 3q^{71} + 8q^{73} - 10q^{76} + 16q^{77} + 13q^{79} - 16q^{80} + 6q^{83} - 20q^{85} + 9q^{89} + 20q^{91} + 2q^{92} - 20q^{95} - 6q^{97} + O(q^{100}) \)

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
0 0 −2.00000 −4.00000 0 −4.00000 0 0 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
\(3\) \(-1\)
\(23\) \(1\)
\(29\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6003))\):

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