Properties

Label 6498.2.a.x
Level $6498$
Weight $2$
Character orbit 6498.a
Self dual yes
Analytic conductor $51.887$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6498 = 2 \cdot 3^{2} \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6498.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(51.8867912334\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 114)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{4} + 4q^{5} - 3q^{7} + q^{8} + O(q^{10}) \) \( q + q^{2} + q^{4} + 4q^{5} - 3q^{7} + q^{8} + 4q^{10} - 2q^{11} + 7q^{13} - 3q^{14} + q^{16} + 4q^{20} - 2q^{22} + 4q^{23} + 11q^{25} + 7q^{26} - 3q^{28} + 4q^{29} - q^{31} + q^{32} - 12q^{35} - 7q^{37} + 4q^{40} + 4q^{41} + 7q^{43} - 2q^{44} + 4q^{46} - 2q^{47} + 2q^{49} + 11q^{50} + 7q^{52} - 4q^{53} - 8q^{55} - 3q^{56} + 4q^{58} - 6q^{59} - q^{61} - q^{62} + q^{64} + 28q^{65} - 3q^{67} - 12q^{70} + 2q^{71} - 3q^{73} - 7q^{74} + 6q^{77} - 5q^{79} + 4q^{80} + 4q^{82} + 12q^{83} + 7q^{86} - 2q^{88} + 18q^{89} - 21q^{91} + 4q^{92} - 2q^{94} - 10q^{97} + 2q^{98} + O(q^{100}) \)

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 4.00000 0 −3.00000 1.00000 0 4.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(19\) \(-1\)

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 6498.2.a.x 1
3.b odd 2 1 2166.2.a.c 1
19.b odd 2 1 6498.2.a.l 1
19.d odd 6 2 342.2.g.d 2
57.d even 2 1 2166.2.a.f 1
57.f even 6 2 114.2.e.a 2
76.f even 6 2 2736.2.s.c 2
228.n odd 6 2 912.2.q.d 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
114.2.e.a 2 57.f even 6 2
342.2.g.d 2 19.d odd 6 2
912.2.q.d 2 228.n odd 6 2
2166.2.a.c 1 3.b odd 2 1
2166.2.a.f 1 57.d even 2 1
2736.2.s.c 2 76.f even 6 2
6498.2.a.l 1 19.b odd 2 1
6498.2.a.x 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6498))\):

\( T_{5} - 4 \)
\( T_{7} + 3 \)
\( T_{11} + 2 \)
\( T_{13} - 7 \)
\( T_{29} - 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( T \)
$5$ \( -4 + T \)
$7$ \( 3 + T \)
$11$ \( 2 + T \)
$13$ \( -7 + T \)
$17$ \( T \)
$19$ \( T \)
$23$ \( -4 + T \)
$29$ \( -4 + T \)
$31$ \( 1 + T \)
$37$ \( 7 + T \)
$41$ \( -4 + T \)
$43$ \( -7 + T \)
$47$ \( 2 + T \)
$53$ \( 4 + T \)
$59$ \( 6 + T \)
$61$ \( 1 + T \)
$67$ \( 3 + T \)
$71$ \( -2 + T \)
$73$ \( 3 + T \)
$79$ \( 5 + T \)
$83$ \( -12 + T \)
$89$ \( -18 + T \)
$97$ \( 10 + T \)
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