Properties

Label 6498.2.a.m
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 722)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{4} - 2 q^{5} - 3 q^{7} + q^{8}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} + q^{4} - 2 q^{5} - 3 q^{7} + q^{8} - 2 q^{10} + 2 q^{11} + 3 q^{13} - 3 q^{14} + q^{16} + q^{17} - 2 q^{20} + 2 q^{22} - 5 q^{23} - q^{25} + 3 q^{26} - 3 q^{28} - 3 q^{29} + 6 q^{31} + q^{32} + q^{34} + 6 q^{35} - 6 q^{37} - 2 q^{40} + 12 q^{41} - 10 q^{43} + 2 q^{44} - 5 q^{46} + 8 q^{47} + 2 q^{49} - q^{50} + 3 q^{52} - 3 q^{53} - 4 q^{55} - 3 q^{56} - 3 q^{58} + 3 q^{59} + 6 q^{62} + q^{64} - 6 q^{65} - 15 q^{67} + q^{68} + 6 q^{70} - 11 q^{73} - 6 q^{74} - 6 q^{77} + 12 q^{79} - 2 q^{80} + 12 q^{82} - 2 q^{83} - 2 q^{85} - 10 q^{86} + 2 q^{88} + 6 q^{89} - 9 q^{91} - 5 q^{92} + 8 q^{94} - 12 q^{97} + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

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 −2.00000 0 −3.00000 1.00000 0 −2.00000
\(n\): 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.m 1
3.b odd 2 1 722.2.a.a 1
12.b even 2 1 5776.2.a.q 1
19.b odd 2 1 6498.2.a.a 1
57.d even 2 1 722.2.a.f yes 1
57.f even 6 2 722.2.c.a 2
57.h odd 6 2 722.2.c.g 2
57.j even 18 6 722.2.e.g 6
57.l odd 18 6 722.2.e.h 6
228.b odd 2 1 5776.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
722.2.a.a 1 3.b odd 2 1
722.2.a.f yes 1 57.d even 2 1
722.2.c.a 2 57.f even 6 2
722.2.c.g 2 57.h odd 6 2
722.2.e.g 6 57.j even 18 6
722.2.e.h 6 57.l odd 18 6
5776.2.a.a 1 228.b odd 2 1
5776.2.a.q 1 12.b even 2 1
6498.2.a.a 1 19.b odd 2 1
6498.2.a.m 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6498))\):

\( T_{5} + 2 \) Copy content Toggle raw display
\( T_{7} + 3 \) Copy content Toggle raw display
\( T_{11} - 2 \) Copy content Toggle raw display
\( T_{13} - 3 \) Copy content Toggle raw display
\( T_{29} + 3 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T - 1 \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T + 2 \) Copy content Toggle raw display
$7$ \( T + 3 \) Copy content Toggle raw display
$11$ \( T - 2 \) Copy content Toggle raw display
$13$ \( T - 3 \) Copy content Toggle raw display
$17$ \( T - 1 \) Copy content Toggle raw display
$19$ \( T \) Copy content Toggle raw display
$23$ \( T + 5 \) Copy content Toggle raw display
$29$ \( T + 3 \) Copy content Toggle raw display
$31$ \( T - 6 \) Copy content Toggle raw display
$37$ \( T + 6 \) Copy content Toggle raw display
$41$ \( T - 12 \) Copy content Toggle raw display
$43$ \( T + 10 \) Copy content Toggle raw display
$47$ \( T - 8 \) Copy content Toggle raw display
$53$ \( T + 3 \) Copy content Toggle raw display
$59$ \( T - 3 \) Copy content Toggle raw display
$61$ \( T \) Copy content Toggle raw display
$67$ \( T + 15 \) Copy content Toggle raw display
$71$ \( T \) Copy content Toggle raw display
$73$ \( T + 11 \) Copy content Toggle raw display
$79$ \( T - 12 \) Copy content Toggle raw display
$83$ \( T + 2 \) Copy content Toggle raw display
$89$ \( T - 6 \) Copy content Toggle raw display
$97$ \( T + 12 \) Copy content Toggle raw display
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