Properties

Label 6003.2.a.c
Level $6003$
Weight $2$
Character orbit 6003.a
Self dual yes
Analytic conductor $47.934$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

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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: \( 1 \)
Twist minimal: no (minimal twist has level 2001)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{4} - 3q^{5} - 3q^{8} + O(q^{10}) \) \( q + q^{2} - q^{4} - 3q^{5} - 3q^{8} - 3q^{10} - 3q^{11} + 3q^{13} - q^{16} + 8q^{19} + 3q^{20} - 3q^{22} + q^{23} + 4q^{25} + 3q^{26} - q^{29} + 7q^{31} + 5q^{32} - 5q^{37} + 8q^{38} + 9q^{40} - 3q^{41} + 2q^{43} + 3q^{44} + q^{46} + 6q^{47} - 7q^{49} + 4q^{50} - 3q^{52} + 2q^{53} + 9q^{55} - q^{58} - q^{59} + 7q^{61} + 7q^{62} + 7q^{64} - 9q^{65} - 9q^{67} - 3q^{71} - 12q^{73} - 5q^{74} - 8q^{76} - 14q^{79} + 3q^{80} - 3q^{82} - 14q^{83} + 2q^{86} + 9q^{88} + 10q^{89} - q^{92} + 6q^{94} - 24q^{95} + 14q^{97} - 7q^{98} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(23\) \(-1\)
\(29\) \(1\)

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 6003.2.a.c 1
3.b odd 2 1 2001.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2001.2.a.a 1 3.b odd 2 1
6003.2.a.c 1 1.a even 1 1 trivial

Hecke kernels

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

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

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( T \)
$5$ \( 3 + T \)
$7$ \( T \)
$11$ \( 3 + T \)
$13$ \( -3 + T \)
$17$ \( T \)
$19$ \( -8 + T \)
$23$ \( -1 + T \)
$29$ \( 1 + T \)
$31$ \( -7 + T \)
$37$ \( 5 + T \)
$41$ \( 3 + T \)
$43$ \( -2 + T \)
$47$ \( -6 + T \)
$53$ \( -2 + T \)
$59$ \( 1 + T \)
$61$ \( -7 + T \)
$67$ \( 9 + T \)
$71$ \( 3 + T \)
$73$ \( 12 + T \)
$79$ \( 14 + T \)
$83$ \( 14 + T \)
$89$ \( -10 + T \)
$97$ \( -14 + T \)
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