Properties

Label 6762.2.a.x
Level $6762$
Weight $2$
Character orbit 6762.a
Self dual yes
Analytic conductor $53.995$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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: no (minimal twist has level 966)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

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
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.x 1
7.b odd 2 1 6762.2.a.bm 1
7.c even 3 2 966.2.i.d 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
966.2.i.d 2 7.c even 3 2
6762.2.a.x 1 1.a even 1 1 trivial
6762.2.a.bm 1 7.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6762))\):

\( T_{5} + 3 \)
\( T_{11} - 1 \)
\( T_{13} + 6 \)
\( T_{17} + 2 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( 1 + T \)
$5$ \( 3 + T \)
$7$ \( T \)
$11$ \( -1 + T \)
$13$ \( 6 + T \)
$17$ \( 2 + T \)
$19$ \( 2 + T \)
$23$ \( 1 + T \)
$29$ \( 7 + T \)
$31$ \( -7 + T \)
$37$ \( 2 + T \)
$41$ \( 10 + T \)
$43$ \( -2 + T \)
$47$ \( -6 + T \)
$53$ \( -11 + T \)
$59$ \( -15 + T \)
$61$ \( 2 + T \)
$67$ \( -2 + T \)
$71$ \( T \)
$73$ \( 10 + T \)
$79$ \( 11 + T \)
$83$ \( -13 + T \)
$89$ \( -8 + T \)
$97$ \( -1 + T \)
show more
show less