Properties

Label 2496.2.a.f
Level $2496$
Weight $2$
Character orbit 2496.a
Self dual yes
Analytic conductor $19.931$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2496.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(19.9306603445\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1248)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{3} - 2q^{7} + q^{9} + O(q^{10}) \) \( q - q^{3} - 2q^{7} + q^{9} + 4q^{11} - q^{13} - 6q^{17} + 6q^{19} + 2q^{21} - 5q^{25} - q^{27} + 2q^{29} + 6q^{31} - 4q^{33} - 10q^{37} + q^{39} + 8q^{41} + 12q^{43} - 12q^{47} - 3q^{49} + 6q^{51} + 6q^{53} - 6q^{57} - 2q^{61} - 2q^{63} + 2q^{67} + 8q^{71} + 14q^{73} + 5q^{75} - 8q^{77} - 4q^{79} + q^{81} + 8q^{83} - 2q^{87} + 4q^{89} + 2q^{91} - 6q^{93} + 14q^{97} + 4q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(1\)
\(13\) \(1\)

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 2496.2.a.f 1
3.b odd 2 1 7488.2.a.z 1
4.b odd 2 1 2496.2.a.y 1
8.b even 2 1 1248.2.a.h yes 1
8.d odd 2 1 1248.2.a.d 1
12.b even 2 1 7488.2.a.bg 1
24.f even 2 1 3744.2.a.i 1
24.h odd 2 1 3744.2.a.h 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1248.2.a.d 1 8.d odd 2 1
1248.2.a.h yes 1 8.b even 2 1
2496.2.a.f 1 1.a even 1 1 trivial
2496.2.a.y 1 4.b odd 2 1
3744.2.a.h 1 24.h odd 2 1
3744.2.a.i 1 24.f even 2 1
7488.2.a.z 1 3.b odd 2 1
7488.2.a.bg 1 12.b even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2496))\):

\( T_{5} \)
\( T_{7} + 2 \)
\( T_{11} - 4 \)
\( T_{17} + 6 \)
\( T_{19} - 6 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( 1 + T \)
$5$ \( T \)
$7$ \( 2 + T \)
$11$ \( -4 + T \)
$13$ \( 1 + T \)
$17$ \( 6 + T \)
$19$ \( -6 + T \)
$23$ \( T \)
$29$ \( -2 + T \)
$31$ \( -6 + T \)
$37$ \( 10 + T \)
$41$ \( -8 + T \)
$43$ \( -12 + T \)
$47$ \( 12 + T \)
$53$ \( -6 + T \)
$59$ \( T \)
$61$ \( 2 + T \)
$67$ \( -2 + T \)
$71$ \( -8 + T \)
$73$ \( -14 + T \)
$79$ \( 4 + T \)
$83$ \( -8 + T \)
$89$ \( -4 + T \)
$97$ \( -14 + T \)
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