Properties

Label 7406.2.a.b
Level $7406$
Weight $2$
Character orbit 7406.a
Self dual yes
Analytic conductor $59.137$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7406 = 2 \cdot 7 \cdot 23^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7406.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(59.1372077370\)
Analytic rank: \(0\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - q^{7} - q^{8} - 3 q^{9} + O(q^{10}) \) \( q - q^{2} + q^{4} - q^{7} - q^{8} - 3 q^{9} + 4 q^{11} - 2 q^{13} + q^{14} + q^{16} - 4 q^{17} + 3 q^{18} - 4 q^{19} - 4 q^{22} - 5 q^{25} + 2 q^{26} - q^{28} + 2 q^{29} + 4 q^{31} - q^{32} + 4 q^{34} - 3 q^{36} - 4 q^{37} + 4 q^{38} - 6 q^{41} + 4 q^{43} + 4 q^{44} + 4 q^{47} + q^{49} + 5 q^{50} - 2 q^{52} - 12 q^{53} + q^{56} - 2 q^{58} + 8 q^{59} - 4 q^{62} + 3 q^{63} + q^{64} - 4 q^{67} - 4 q^{68} + 8 q^{71} + 3 q^{72} - 10 q^{73} + 4 q^{74} - 4 q^{76} - 4 q^{77} + 8 q^{79} + 9 q^{81} + 6 q^{82} + 12 q^{83} - 4 q^{86} - 4 q^{88} + 4 q^{89} + 2 q^{91} - 4 q^{94} - 12 q^{97} - q^{98} - 12 q^{99} + O(q^{100}) \)

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
−1.00000 0 1.00000 0 0 −1.00000 −1.00000 −3.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(7\) \(1\)
\(23\) \(-1\)

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 7406.2.a.b 1
23.b odd 2 1 7406.2.a.c yes 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
7406.2.a.b 1 1.a even 1 1 trivial
7406.2.a.c yes 1 23.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(7406))\):

\( T_{3} \)
\( T_{5} \)
\( T_{11} - 4 \)

Hecke characteristic polynomials

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