Properties

Label 9240.2.a.bi
Level $9240$
Weight $2$
Character orbit 9240.a
Self dual yes
Analytic conductor $73.782$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 9240 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9240.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(73.7817714677\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \( q + q^{3} + q^{5} + q^{7} + q^{9} + O(q^{10}) \) \( q + q^{3} + q^{5} + q^{7} + q^{9} - q^{11} - 2 q^{13} + q^{15} - 6 q^{17} - 4 q^{19} + q^{21} + q^{25} + q^{27} + 6 q^{29} - q^{33} + q^{35} - 10 q^{37} - 2 q^{39} + 2 q^{41} + 4 q^{43} + q^{45} + q^{49} - 6 q^{51} + 6 q^{53} - q^{55} - 4 q^{57} - 4 q^{59} - 2 q^{61} + q^{63} - 2 q^{65} - 4 q^{67} - 16 q^{71} + 2 q^{73} + q^{75} - q^{77} + q^{81} + 12 q^{83} - 6 q^{85} + 6 q^{87} - 6 q^{89} - 2 q^{91} - 4 q^{95} + 2 q^{97} - q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(5\) \(-1\)
\(7\) \(-1\)
\(11\) \(1\)

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 9240.2.a.bi 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
9240.2.a.bi 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(9240))\):

\( T_{13} + 2 \)
\( T_{17} + 6 \)
\( T_{19} + 4 \)
\( T_{23} \)
\( T_{37} + 10 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( -1 + T \)
$5$ \( -1 + T \)
$7$ \( -1 + T \)
$11$ \( 1 + T \)
$13$ \( 2 + T \)
$17$ \( 6 + T \)
$19$ \( 4 + T \)
$23$ \( T \)
$29$ \( -6 + T \)
$31$ \( T \)
$37$ \( 10 + T \)
$41$ \( -2 + T \)
$43$ \( -4 + T \)
$47$ \( T \)
$53$ \( -6 + T \)
$59$ \( 4 + T \)
$61$ \( 2 + T \)
$67$ \( 4 + T \)
$71$ \( 16 + T \)
$73$ \( -2 + T \)
$79$ \( T \)
$83$ \( -12 + T \)
$89$ \( 6 + T \)
$97$ \( -2 + T \)
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