Properties

Label 6762.2.a.k
Level $6762$
Weight $2$
Character orbit 6762.a
Self dual yes
Analytic conductor $53.995$
Analytic rank $0$
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: \(0\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} - 3q^{5} - q^{6} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + q^{3} + q^{4} - 3q^{5} - q^{6} - q^{8} + q^{9} + 3q^{10} + 2q^{11} + q^{12} + 7q^{13} - 3q^{15} + q^{16} - 4q^{17} - q^{18} + 6q^{19} - 3q^{20} - 2q^{22} + q^{23} - q^{24} + 4q^{25} - 7q^{26} + q^{27} + 7q^{29} + 3q^{30} + 8q^{31} - q^{32} + 2q^{33} + 4q^{34} + q^{36} - 5q^{37} - 6q^{38} + 7q^{39} + 3q^{40} - 5q^{41} - 5q^{43} + 2q^{44} - 3q^{45} - q^{46} - 3q^{47} + q^{48} - 4q^{50} - 4q^{51} + 7q^{52} + 6q^{53} - q^{54} - 6q^{55} + 6q^{57} - 7q^{58} + 8q^{59} - 3q^{60} - 12q^{61} - 8q^{62} + q^{64} - 21q^{65} - 2q^{66} + 8q^{67} - 4q^{68} + q^{69} - 12q^{71} - q^{72} + 14q^{73} + 5q^{74} + 4q^{75} + 6q^{76} - 7q^{78} - 6q^{79} - 3q^{80} + q^{81} + 5q^{82} - 12q^{83} + 12q^{85} + 5q^{86} + 7q^{87} - 2q^{88} + 8q^{89} + 3q^{90} + q^{92} + 8q^{93} + 3q^{94} - 18q^{95} - q^{96} + 3q^{97} + 2q^{99} + O(q^{100}) \)

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 1.00000 1.00000 −3.00000 −1.00000 0 −1.00000 1.00000 3.00000
\(n\): 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.k yes 1
7.b odd 2 1 6762.2.a.j 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6762.2.a.j 1 7.b odd 2 1
6762.2.a.k yes 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6762))\):

\( T_{5} + 3 \)
\( T_{11} - 2 \)
\( T_{13} - 7 \)
\( T_{17} + 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( -1 + T \)
$5$ \( 3 + T \)
$7$ \( T \)
$11$ \( -2 + T \)
$13$ \( -7 + T \)
$17$ \( 4 + T \)
$19$ \( -6 + T \)
$23$ \( -1 + T \)
$29$ \( -7 + T \)
$31$ \( -8 + T \)
$37$ \( 5 + T \)
$41$ \( 5 + T \)
$43$ \( 5 + T \)
$47$ \( 3 + T \)
$53$ \( -6 + T \)
$59$ \( -8 + T \)
$61$ \( 12 + T \)
$67$ \( -8 + T \)
$71$ \( 12 + T \)
$73$ \( -14 + T \)
$79$ \( 6 + T \)
$83$ \( 12 + T \)
$89$ \( -8 + T \)
$97$ \( -3 + T \)
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