Properties

Label 2960.2.a.f
Level $2960$
Weight $2$
Character orbit 2960.a
Self dual yes
Analytic conductor $23.636$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2960 = 2^{4} \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2960.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(23.6357189983\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1480)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{3} + q^{5} + q^{7} - 2q^{9} + O(q^{10}) \) \( q - q^{3} + q^{5} + q^{7} - 2q^{9} + 3q^{11} - q^{15} - 8q^{17} - q^{21} + 4q^{23} + q^{25} + 5q^{27} - 8q^{29} - 6q^{31} - 3q^{33} + q^{35} + q^{37} + 3q^{41} - 2q^{43} - 2q^{45} - 3q^{47} - 6q^{49} + 8q^{51} - q^{53} + 3q^{55} + 4q^{59} - 6q^{61} - 2q^{63} - 4q^{67} - 4q^{69} + q^{71} + 9q^{73} - q^{75} + 3q^{77} - 10q^{79} + q^{81} - 5q^{83} - 8q^{85} + 8q^{87} + 6q^{89} + 6q^{93} - 10q^{97} - 6q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(5\) \(-1\)
\(37\) \(-1\)

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 2960.2.a.f 1
4.b odd 2 1 1480.2.a.c 1
20.d odd 2 1 7400.2.a.c 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1480.2.a.c 1 4.b odd 2 1
2960.2.a.f 1 1.a even 1 1 trivial
7400.2.a.c 1 20.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2960))\):

\( T_{3} + 1 \)
\( T_{7} - 1 \)
\( T_{13} \)

Hecke characteristic polynomials

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