Properties

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

Related objects

Downloads

Learn more

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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} + q^{7} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} + q^{7} - q^{8} + 2q^{11} + 3q^{13} - q^{14} + q^{16} - 4q^{17} - 2q^{22} - 4q^{23} - 5q^{25} - 3q^{26} + q^{28} + 3q^{31} - q^{32} + 4q^{34} + 5q^{37} + 4q^{41} - 9q^{43} + 2q^{44} + 4q^{46} - 10q^{47} - 6q^{49} + 5q^{50} + 3q^{52} - 4q^{53} - q^{56} - 14q^{59} + 11q^{61} - 3q^{62} + q^{64} - 3q^{67} - 4q^{68} + 14q^{71} - 11q^{73} - 5q^{74} + 2q^{77} - q^{79} - 4q^{82} - 8q^{83} + 9q^{86} - 2q^{88} - 14q^{89} + 3q^{91} - 4q^{92} + 10q^{94} - 2q^{97} + 6q^{98} + O(q^{100}) \)

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 1.00000 −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.g 1
3.b odd 2 1 2166.2.a.h 1
19.b odd 2 1 6498.2.a.u 1
19.d odd 6 2 342.2.g.c 2
57.d even 2 1 2166.2.a.b 1
57.f even 6 2 114.2.e.b 2
76.f even 6 2 2736.2.s.k 2
228.n odd 6 2 912.2.q.b 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
114.2.e.b 2 57.f even 6 2
342.2.g.c 2 19.d odd 6 2
912.2.q.b 2 228.n odd 6 2
2166.2.a.b 1 57.d even 2 1
2166.2.a.h 1 3.b odd 2 1
2736.2.s.k 2 76.f even 6 2
6498.2.a.g 1 1.a even 1 1 trivial
6498.2.a.u 1 19.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6498))\):

\( T_{5} \)
\( T_{7} - 1 \)
\( T_{11} - 2 \)
\( T_{13} - 3 \)
\( T_{29} \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( T \)
$5$ \( T \)
$7$ \( -1 + T \)
$11$ \( -2 + T \)
$13$ \( -3 + T \)
$17$ \( 4 + T \)
$19$ \( T \)
$23$ \( 4 + T \)
$29$ \( T \)
$31$ \( -3 + T \)
$37$ \( -5 + T \)
$41$ \( -4 + T \)
$43$ \( 9 + T \)
$47$ \( 10 + T \)
$53$ \( 4 + T \)
$59$ \( 14 + T \)
$61$ \( -11 + T \)
$67$ \( 3 + T \)
$71$ \( -14 + T \)
$73$ \( 11 + T \)
$79$ \( 1 + T \)
$83$ \( 8 + T \)
$89$ \( 14 + T \)
$97$ \( 2 + T \)
show more
show less