Properties

Label 6762.2.a.r
Level $6762$
Weight $2$
Character orbit 6762.a
Self dual yes
Analytic conductor $53.995$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6762.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(53.9948418468\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 966)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} + 2q^{5} - q^{6} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + q^{3} + q^{4} + 2q^{5} - q^{6} - q^{8} + q^{9} - 2q^{10} + q^{12} - 4q^{13} + 2q^{15} + q^{16} - q^{18} - 6q^{19} + 2q^{20} - q^{23} - q^{24} - q^{25} + 4q^{26} + q^{27} - 6q^{29} - 2q^{30} + 10q^{31} - q^{32} + q^{36} - 6q^{37} + 6q^{38} - 4q^{39} - 2q^{40} + 2q^{41} + 12q^{43} + 2q^{45} + q^{46} - 10q^{47} + q^{48} + q^{50} - 4q^{52} - 10q^{53} - q^{54} - 6q^{57} + 6q^{58} + 12q^{59} + 2q^{60} + 14q^{61} - 10q^{62} + q^{64} - 8q^{65} - 12q^{67} - q^{69} - 12q^{71} - q^{72} - 14q^{73} + 6q^{74} - q^{75} - 6q^{76} + 4q^{78} + 2q^{80} + q^{81} - 2q^{82} - 2q^{83} - 12q^{86} - 6q^{87} + 12q^{89} - 2q^{90} - q^{92} + 10q^{93} + 10q^{94} - 12q^{95} - q^{96} - 12q^{97} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(-1\)
\(7\) \(-1\)
\(23\) \(1\)

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 6762.2.a.r 1
7.b odd 2 1 966.2.a.b 1
21.c even 2 1 2898.2.a.r 1
28.d even 2 1 7728.2.a.p 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
966.2.a.b 1 7.b odd 2 1
2898.2.a.r 1 21.c even 2 1
6762.2.a.r 1 1.a even 1 1 trivial
7728.2.a.p 1 28.d even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6762))\):

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

Hecke characteristic polynomials

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