Properties

Label 6292.2.a.g
Level $6292$
Weight $2$
Character orbit 6292.a
Self dual yes
Analytic conductor $50.242$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6292 = 2^{2} \cdot 11^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6292.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(50.2418729518\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 52)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2 q^{5} + 2 q^{7} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q + 2 q^{5} + 2 q^{7} - 3 q^{9} + q^{13} - 6 q^{17} + 6 q^{19} + 8 q^{23} - q^{25} - 2 q^{29} + 10 q^{31} + 4 q^{35} - 6 q^{37} + 6 q^{41} - 4 q^{43} - 6 q^{45} - 2 q^{47} - 3 q^{49} + 6 q^{53} - 10 q^{59} + 2 q^{61} - 6 q^{63} + 2 q^{65} + 10 q^{67} + 10 q^{71} - 2 q^{73} + 4 q^{79} + 9 q^{81} + 6 q^{83} - 12 q^{85} - 6 q^{89} + 2 q^{91} + 12 q^{95} + 2 q^{97}+O(q^{100}) \) 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
0 0 0 2.00000 0 2.00000 0 −3.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(11\) \(-1\)
\(13\) \(-1\)

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 6292.2.a.g 1
11.b odd 2 1 52.2.a.a 1
33.d even 2 1 468.2.a.b 1
44.c even 2 1 208.2.a.c 1
55.d odd 2 1 1300.2.a.d 1
55.e even 4 2 1300.2.c.c 2
77.b even 2 1 2548.2.a.e 1
77.h odd 6 2 2548.2.j.e 2
77.i even 6 2 2548.2.j.f 2
88.b odd 2 1 832.2.a.e 1
88.g even 2 1 832.2.a.f 1
99.g even 6 2 4212.2.i.i 2
99.h odd 6 2 4212.2.i.d 2
132.d odd 2 1 1872.2.a.f 1
143.d odd 2 1 676.2.a.c 1
143.g even 4 2 676.2.d.c 2
143.i odd 6 2 676.2.e.b 2
143.k odd 6 2 676.2.e.c 2
143.o even 12 4 676.2.h.c 4
176.i even 4 2 3328.2.b.e 2
176.l odd 4 2 3328.2.b.q 2
220.g even 2 1 5200.2.a.q 1
264.m even 2 1 7488.2.a.bn 1
264.p odd 2 1 7488.2.a.bw 1
429.e even 2 1 6084.2.a.m 1
429.l odd 4 2 6084.2.b.m 2
572.b even 2 1 2704.2.a.g 1
572.k odd 4 2 2704.2.f.f 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
52.2.a.a 1 11.b odd 2 1
208.2.a.c 1 44.c even 2 1
468.2.a.b 1 33.d even 2 1
676.2.a.c 1 143.d odd 2 1
676.2.d.c 2 143.g even 4 2
676.2.e.b 2 143.i odd 6 2
676.2.e.c 2 143.k odd 6 2
676.2.h.c 4 143.o even 12 4
832.2.a.e 1 88.b odd 2 1
832.2.a.f 1 88.g even 2 1
1300.2.a.d 1 55.d odd 2 1
1300.2.c.c 2 55.e even 4 2
1872.2.a.f 1 132.d odd 2 1
2548.2.a.e 1 77.b even 2 1
2548.2.j.e 2 77.h odd 6 2
2548.2.j.f 2 77.i even 6 2
2704.2.a.g 1 572.b even 2 1
2704.2.f.f 2 572.k odd 4 2
3328.2.b.e 2 176.i even 4 2
3328.2.b.q 2 176.l odd 4 2
4212.2.i.d 2 99.h odd 6 2
4212.2.i.i 2 99.g even 6 2
5200.2.a.q 1 220.g even 2 1
6084.2.a.m 1 429.e even 2 1
6084.2.b.m 2 429.l odd 4 2
6292.2.a.g 1 1.a even 1 1 trivial
7488.2.a.bn 1 264.m even 2 1
7488.2.a.bw 1 264.p odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6292))\):

\( T_{3} \) Copy content Toggle raw display
\( T_{5} - 2 \) Copy content Toggle raw display
\( T_{7} - 2 \) Copy content Toggle raw display
\( T_{17} + 6 \) Copy content Toggle raw display

Hecke characteristic polynomials

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