Properties

Label 7440.2.a.q
Level $7440$
Weight $2$
Character orbit 7440.a
Self dual yes
Analytic conductor $59.409$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7440 = 2^{4} \cdot 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7440.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(59.4086991038\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 930)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} - q^{5} + q^{9} + O(q^{10}) \) \( q + q^{3} - q^{5} + q^{9} + 4 q^{11} + 6 q^{13} - q^{15} + 2 q^{17} + 4 q^{19} + 4 q^{23} + q^{25} + q^{27} + 2 q^{29} + q^{31} + 4 q^{33} - 2 q^{37} + 6 q^{39} - 6 q^{41} + 4 q^{43} - q^{45} - 7 q^{49} + 2 q^{51} + 2 q^{53} - 4 q^{55} + 4 q^{57} + 4 q^{59} - 6 q^{61} - 6 q^{65} - 16 q^{67} + 4 q^{69} + 12 q^{71} - 6 q^{73} + q^{75} + 16 q^{79} + q^{81} + 12 q^{83} - 2 q^{85} + 2 q^{87} - 18 q^{89} + q^{93} - 4 q^{95} - 14 q^{97} + 4 q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(5\) \(1\)
\(31\) \(-1\)

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 7440.2.a.q 1
4.b odd 2 1 930.2.a.b 1
12.b even 2 1 2790.2.a.ba 1
20.d odd 2 1 4650.2.a.bp 1
20.e even 4 2 4650.2.d.o 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
930.2.a.b 1 4.b odd 2 1
2790.2.a.ba 1 12.b even 2 1
4650.2.a.bp 1 20.d odd 2 1
4650.2.d.o 2 20.e even 4 2
7440.2.a.q 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(7440))\):

\( T_{7} \)
\( T_{11} - 4 \)
\( T_{13} - 6 \)
\( T_{17} - 2 \)
\( T_{19} - 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( -1 + T \)
$5$ \( 1 + T \)
$7$ \( T \)
$11$ \( -4 + T \)
$13$ \( -6 + T \)
$17$ \( -2 + T \)
$19$ \( -4 + T \)
$23$ \( -4 + T \)
$29$ \( -2 + T \)
$31$ \( -1 + T \)
$37$ \( 2 + T \)
$41$ \( 6 + T \)
$43$ \( -4 + T \)
$47$ \( T \)
$53$ \( -2 + T \)
$59$ \( -4 + T \)
$61$ \( 6 + T \)
$67$ \( 16 + T \)
$71$ \( -12 + T \)
$73$ \( 6 + T \)
$79$ \( -16 + T \)
$83$ \( -12 + T \)
$89$ \( 18 + T \)
$97$ \( 14 + T \)
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