Properties

Label 6534.2.a.b
Level $6534$
Weight $2$
Character orbit 6534.a
Self dual yes
Analytic conductor $52.174$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 6534 = 2 \cdot 3^{3} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6534.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(52.1742526807\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 54)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - 3 q^{5} + q^{7} - q^{8}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} + q^{4} - 3 q^{5} + q^{7} - q^{8} + 3 q^{10} + 4 q^{13} - q^{14} + q^{16} - 2 q^{19} - 3 q^{20} + 6 q^{23} + 4 q^{25} - 4 q^{26} + q^{28} + 6 q^{29} + 5 q^{31} - q^{32} - 3 q^{35} + 2 q^{37} + 2 q^{38} + 3 q^{40} - 6 q^{41} + 10 q^{43} - 6 q^{46} - 6 q^{47} - 6 q^{49} - 4 q^{50} + 4 q^{52} - 9 q^{53} - q^{56} - 6 q^{58} - 12 q^{59} - 8 q^{61} - 5 q^{62} + q^{64} - 12 q^{65} + 14 q^{67} + 3 q^{70} + 7 q^{73} - 2 q^{74} - 2 q^{76} - 8 q^{79} - 3 q^{80} + 6 q^{82} - 3 q^{83} - 10 q^{86} + 18 q^{89} + 4 q^{91} + 6 q^{92} + 6 q^{94} + 6 q^{95} - q^{97} + 6 q^{98}+O(q^{100}) \) 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 −3.00000 0 1.00000 −1.00000 0 3.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(1\)
\(11\) \(-1\)

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 6534.2.a.b 1
3.b odd 2 1 6534.2.a.bc 1
11.b odd 2 1 54.2.a.b yes 1
33.d even 2 1 54.2.a.a 1
44.c even 2 1 432.2.a.b 1
55.d odd 2 1 1350.2.a.h 1
55.e even 4 2 1350.2.c.k 2
77.b even 2 1 2646.2.a.bd 1
88.b odd 2 1 1728.2.a.y 1
88.g even 2 1 1728.2.a.z 1
99.g even 6 2 162.2.c.c 2
99.h odd 6 2 162.2.c.b 2
132.d odd 2 1 432.2.a.g 1
143.d odd 2 1 9126.2.a.r 1
165.d even 2 1 1350.2.a.r 1
165.l odd 4 2 1350.2.c.b 2
231.h odd 2 1 2646.2.a.a 1
264.m even 2 1 1728.2.a.c 1
264.p odd 2 1 1728.2.a.d 1
396.k even 6 2 1296.2.i.o 2
396.o odd 6 2 1296.2.i.c 2
429.e even 2 1 9126.2.a.u 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
54.2.a.a 1 33.d even 2 1
54.2.a.b yes 1 11.b odd 2 1
162.2.c.b 2 99.h odd 6 2
162.2.c.c 2 99.g even 6 2
432.2.a.b 1 44.c even 2 1
432.2.a.g 1 132.d odd 2 1
1296.2.i.c 2 396.o odd 6 2
1296.2.i.o 2 396.k even 6 2
1350.2.a.h 1 55.d odd 2 1
1350.2.a.r 1 165.d even 2 1
1350.2.c.b 2 165.l odd 4 2
1350.2.c.k 2 55.e even 4 2
1728.2.a.c 1 264.m even 2 1
1728.2.a.d 1 264.p odd 2 1
1728.2.a.y 1 88.b odd 2 1
1728.2.a.z 1 88.g even 2 1
2646.2.a.a 1 231.h odd 2 1
2646.2.a.bd 1 77.b even 2 1
6534.2.a.b 1 1.a even 1 1 trivial
6534.2.a.bc 1 3.b odd 2 1
9126.2.a.r 1 143.d odd 2 1
9126.2.a.u 1 429.e even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6534))\):

\( T_{5} + 3 \) Copy content Toggle raw display
\( T_{7} - 1 \) Copy content Toggle raw display
\( T_{13} - 4 \) Copy content Toggle raw display
\( T_{17} \) Copy content Toggle raw display
\( T_{29} - 6 \) 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
$5$ \( T + 3 \) Copy content Toggle raw display
$7$ \( T - 1 \) Copy content Toggle raw display
$11$ \( T \) Copy content Toggle raw display
$13$ \( T - 4 \) Copy content Toggle raw display
$17$ \( T \) Copy content Toggle raw display
$19$ \( T + 2 \) Copy content Toggle raw display
$23$ \( T - 6 \) Copy content Toggle raw display
$29$ \( T - 6 \) Copy content Toggle raw display
$31$ \( T - 5 \) Copy content Toggle raw display
$37$ \( T - 2 \) Copy content Toggle raw display
$41$ \( T + 6 \) Copy content Toggle raw display
$43$ \( T - 10 \) Copy content Toggle raw display
$47$ \( T + 6 \) Copy content Toggle raw display
$53$ \( T + 9 \) Copy content Toggle raw display
$59$ \( T + 12 \) Copy content Toggle raw display
$61$ \( T + 8 \) Copy content Toggle raw display
$67$ \( T - 14 \) Copy content Toggle raw display
$71$ \( T \) Copy content Toggle raw display
$73$ \( T - 7 \) Copy content Toggle raw display
$79$ \( T + 8 \) Copy content Toggle raw display
$83$ \( T + 3 \) Copy content Toggle raw display
$89$ \( T - 18 \) Copy content Toggle raw display
$97$ \( T + 1 \) Copy content Toggle raw display
show more
show less