Properties

Label 6498.2.a.h
Level $6498$
Weight $2$
Character orbit 6498.a
Self dual yes
Analytic conductor $51.887$
Analytic rank $1$
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: \(1\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} + 4q^{7} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} + 4q^{7} - q^{8} - 4q^{11} - 4q^{14} + q^{16} + 2q^{17} + 4q^{22} + 2q^{23} - 5q^{25} + 4q^{28} - 6q^{29} - 6q^{31} - q^{32} - 2q^{34} + 8q^{37} + 10q^{41} - 12q^{43} - 4q^{44} - 2q^{46} - 10q^{47} + 9q^{49} + 5q^{50} + 2q^{53} - 4q^{56} + 6q^{58} + 4q^{59} - 10q^{61} + 6q^{62} + q^{64} + 2q^{68} - 16q^{71} - 2q^{73} - 8q^{74} - 16q^{77} - 10q^{79} - 10q^{82} + 16q^{83} + 12q^{86} + 4q^{88} - 2q^{89} + 2q^{92} + 10q^{94} + 10q^{97} - 9q^{98} + O(q^{100}) \)

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 0 0 4.00000 −1.00000 0 0
\(n\): 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.h 1
3.b odd 2 1 2166.2.a.i 1
19.b odd 2 1 342.2.a.f 1
57.d even 2 1 114.2.a.a 1
76.d even 2 1 2736.2.a.j 1
95.d odd 2 1 8550.2.a.a 1
228.b odd 2 1 912.2.a.h 1
285.b even 2 1 2850.2.a.x 1
285.j odd 4 2 2850.2.d.s 2
399.h odd 2 1 5586.2.a.p 1
456.l odd 2 1 3648.2.a.j 1
456.p even 2 1 3648.2.a.bb 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
114.2.a.a 1 57.d even 2 1
342.2.a.f 1 19.b odd 2 1
912.2.a.h 1 228.b odd 2 1
2166.2.a.i 1 3.b odd 2 1
2736.2.a.j 1 76.d even 2 1
2850.2.a.x 1 285.b even 2 1
2850.2.d.s 2 285.j odd 4 2
3648.2.a.j 1 456.l odd 2 1
3648.2.a.bb 1 456.p even 2 1
5586.2.a.p 1 399.h odd 2 1
6498.2.a.h 1 1.a even 1 1 trivial
8550.2.a.a 1 95.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6498))\):

\( T_{5} \)
\( T_{7} - 4 \)
\( T_{11} + 4 \)
\( T_{13} \)
\( T_{29} + 6 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( T \)
$5$ \( T \)
$7$ \( -4 + T \)
$11$ \( 4 + T \)
$13$ \( T \)
$17$ \( -2 + T \)
$19$ \( T \)
$23$ \( -2 + T \)
$29$ \( 6 + T \)
$31$ \( 6 + T \)
$37$ \( -8 + T \)
$41$ \( -10 + T \)
$43$ \( 12 + T \)
$47$ \( 10 + T \)
$53$ \( -2 + T \)
$59$ \( -4 + T \)
$61$ \( 10 + T \)
$67$ \( T \)
$71$ \( 16 + T \)
$73$ \( 2 + T \)
$79$ \( 10 + T \)
$83$ \( -16 + T \)
$89$ \( 2 + T \)
$97$ \( -10 + T \)
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