Properties

Label 7448.2.a.a
Level $7448$
Weight $2$
Character orbit 7448.a
Self dual yes
Analytic conductor $59.473$
Analytic rank $2$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7448 = 2^{3} \cdot 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7448.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(59.4725794254\)
Analytic rank: \(2\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1064)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2 q^{3} - q^{5} + q^{9} + O(q^{10}) \) \( q - 2 q^{3} - q^{5} + q^{9} - 3 q^{11} - 4 q^{13} + 2 q^{15} - 2 q^{17} - q^{19} - 7 q^{23} - 4 q^{25} + 4 q^{27} + 2 q^{29} - 6 q^{31} + 6 q^{33} - 10 q^{37} + 8 q^{39} - 8 q^{41} + 7 q^{43} - q^{45} - 9 q^{47} + 4 q^{51} + 6 q^{53} + 3 q^{55} + 2 q^{57} - 14 q^{59} - 5 q^{61} + 4 q^{65} + 14 q^{67} + 14 q^{69} + 8 q^{71} - q^{73} + 8 q^{75} + 10 q^{79} - 11 q^{81} - 17 q^{83} + 2 q^{85} - 4 q^{87} + 12 q^{93} + q^{95} - 12 q^{97} - 3 q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(7\) \(-1\)
\(19\) \(1\)

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 7448.2.a.a 1
7.b odd 2 1 7448.2.a.t 1
7.d odd 6 2 1064.2.q.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1064.2.q.a 2 7.d odd 6 2
7448.2.a.a 1 1.a even 1 1 trivial
7448.2.a.t 1 7.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(7448))\):

\( T_{3} + 2 \)
\( T_{5} + 1 \)
\( T_{11} + 3 \)
\( T_{13} + 4 \)
\( T_{17} + 2 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( 2 + T \)
$5$ \( 1 + T \)
$7$ \( T \)
$11$ \( 3 + T \)
$13$ \( 4 + T \)
$17$ \( 2 + T \)
$19$ \( 1 + T \)
$23$ \( 7 + T \)
$29$ \( -2 + T \)
$31$ \( 6 + T \)
$37$ \( 10 + T \)
$41$ \( 8 + T \)
$43$ \( -7 + T \)
$47$ \( 9 + T \)
$53$ \( -6 + T \)
$59$ \( 14 + T \)
$61$ \( 5 + T \)
$67$ \( -14 + T \)
$71$ \( -8 + T \)
$73$ \( 1 + T \)
$79$ \( -10 + T \)
$83$ \( 17 + T \)
$89$ \( T \)
$97$ \( 12 + T \)
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