Properties

Label 7448.2.a.h
Level $7448$
Weight $2$
Character orbit 7448.a
Self dual yes
Analytic conductor $59.473$
Analytic rank $1$
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: \(1\)
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

\(f(q)\) \(=\) \( q - 3q^{5} - 3q^{9} + O(q^{10}) \) \( q - 3q^{5} - 3q^{9} - q^{11} + 6q^{17} + q^{19} - 3q^{23} + 4q^{25} + 6q^{29} - 2q^{31} - 6q^{41} + 9q^{43} + 9q^{45} + 3q^{47} - 2q^{53} + 3q^{55} + 12q^{59} - 11q^{61} - 8q^{67} + 6q^{71} + 15q^{73} - 12q^{79} + 9q^{81} - 7q^{83} - 18q^{85} + 8q^{89} - 3q^{95} + 6q^{97} + 3q^{99} + O(q^{100}) \)

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 0 0 −3.00000 0 0 0 −3.00000 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.h 1
7.b odd 2 1 7448.2.a.n 1
7.d odd 6 2 1064.2.q.d 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1064.2.q.d 2 7.d odd 6 2
7448.2.a.h 1 1.a even 1 1 trivial
7448.2.a.n 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(7448))\):

\( T_{3} \)
\( T_{5} + 3 \)
\( T_{11} + 1 \)
\( T_{13} \)
\( T_{17} - 6 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( 3 + T \)
$7$ \( T \)
$11$ \( 1 + T \)
$13$ \( T \)
$17$ \( -6 + T \)
$19$ \( -1 + T \)
$23$ \( 3 + T \)
$29$ \( -6 + T \)
$31$ \( 2 + T \)
$37$ \( T \)
$41$ \( 6 + T \)
$43$ \( -9 + T \)
$47$ \( -3 + T \)
$53$ \( 2 + T \)
$59$ \( -12 + T \)
$61$ \( 11 + T \)
$67$ \( 8 + T \)
$71$ \( -6 + T \)
$73$ \( -15 + T \)
$79$ \( 12 + T \)
$83$ \( 7 + T \)
$89$ \( -8 + T \)
$97$ \( -6 + T \)
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