Properties

Label 4024.2.a.a
Level $4024$
Weight $2$
Character orbit 4024.a
Self dual yes
Analytic conductor $32.132$
Analytic rank $2$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4024 = 2^{3} \cdot 503 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4024.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1318017734\)
Analytic rank: \(2\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{3} - 5q^{7} - 2q^{9} + O(q^{10}) \) \( q - q^{3} - 5q^{7} - 2q^{9} - 5q^{11} + q^{13} - 4q^{17} - 4q^{19} + 5q^{21} - 9q^{23} - 5q^{25} + 5q^{27} + 2q^{29} + 2q^{31} + 5q^{33} - 6q^{37} - q^{39} + 6q^{41} - 5q^{43} + q^{47} + 18q^{49} + 4q^{51} - 6q^{53} + 4q^{57} - 12q^{59} - 3q^{61} + 10q^{63} - 5q^{67} + 9q^{69} + 6q^{71} - 2q^{73} + 5q^{75} + 25q^{77} - 8q^{79} + q^{81} + 7q^{83} - 2q^{87} + 6q^{89} - 5q^{91} - 2q^{93} + 10q^{97} + 10q^{99} + O(q^{100}) \)

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
0 −1.00000 0 0 0 −5.00000 0 −2.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(503\) \(1\)

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 4024.2.a.a 1
4.b odd 2 1 8048.2.a.i 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4024.2.a.a 1 1.a even 1 1 trivial
8048.2.a.i 1 4.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4024))\):

\( T_{3} + 1 \)
\( T_{5} \)
\( T_{7} + 5 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( 1 + T \)
$5$ \( T \)
$7$ \( 5 + T \)
$11$ \( 5 + T \)
$13$ \( -1 + T \)
$17$ \( 4 + T \)
$19$ \( 4 + T \)
$23$ \( 9 + T \)
$29$ \( -2 + T \)
$31$ \( -2 + T \)
$37$ \( 6 + T \)
$41$ \( -6 + T \)
$43$ \( 5 + T \)
$47$ \( -1 + T \)
$53$ \( 6 + T \)
$59$ \( 12 + T \)
$61$ \( 3 + T \)
$67$ \( 5 + T \)
$71$ \( -6 + T \)
$73$ \( 2 + T \)
$79$ \( 8 + T \)
$83$ \( -7 + T \)
$89$ \( -6 + T \)
$97$ \( -10 + T \)
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