Properties

Label 792.2.a.g
Level $792$
Weight $2$
Character orbit 792.a
Self dual yes
Analytic conductor $6.324$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 792 = 2^{3} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 792.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(6.32415184009\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 88)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 3 q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( q + 3 q^{5} - 2 q^{7} + q^{11} + 6 q^{17} + 4 q^{19} - q^{23} + 4 q^{25} + 8 q^{29} - 7 q^{31} - 6 q^{35} - q^{37} - 4 q^{41} + 6 q^{43} + 8 q^{47} - 3 q^{49} - 2 q^{53} + 3 q^{55} + q^{59} + 4 q^{61} - 5 q^{67} - 3 q^{71} + 16 q^{73} - 2 q^{77} + 2 q^{79} + 2 q^{83} + 18 q^{85} - 15 q^{89} + 12 q^{95} - 7 q^{97}+O(q^{100}) \) 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 3.00000 0 −2.00000 0 0 0
\(n\): 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 792.2.a.g 1
3.b odd 2 1 88.2.a.a 1
4.b odd 2 1 1584.2.a.q 1
8.b even 2 1 6336.2.a.h 1
8.d odd 2 1 6336.2.a.k 1
11.b odd 2 1 8712.2.a.x 1
12.b even 2 1 176.2.a.c 1
15.d odd 2 1 2200.2.a.k 1
15.e even 4 2 2200.2.b.a 2
21.c even 2 1 4312.2.a.l 1
24.f even 2 1 704.2.a.b 1
24.h odd 2 1 704.2.a.l 1
33.d even 2 1 968.2.a.a 1
33.f even 10 4 968.2.i.i 4
33.h odd 10 4 968.2.i.j 4
48.i odd 4 2 2816.2.c.i 2
48.k even 4 2 2816.2.c.d 2
60.h even 2 1 4400.2.a.a 1
60.l odd 4 2 4400.2.b.b 2
84.h odd 2 1 8624.2.a.c 1
132.d odd 2 1 1936.2.a.l 1
264.m even 2 1 7744.2.a.bk 1
264.p odd 2 1 7744.2.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
88.2.a.a 1 3.b odd 2 1
176.2.a.c 1 12.b even 2 1
704.2.a.b 1 24.f even 2 1
704.2.a.l 1 24.h odd 2 1
792.2.a.g 1 1.a even 1 1 trivial
968.2.a.a 1 33.d even 2 1
968.2.i.i 4 33.f even 10 4
968.2.i.j 4 33.h odd 10 4
1584.2.a.q 1 4.b odd 2 1
1936.2.a.l 1 132.d odd 2 1
2200.2.a.k 1 15.d odd 2 1
2200.2.b.a 2 15.e even 4 2
2816.2.c.d 2 48.k even 4 2
2816.2.c.i 2 48.i odd 4 2
4312.2.a.l 1 21.c even 2 1
4400.2.a.a 1 60.h even 2 1
4400.2.b.b 2 60.l odd 4 2
6336.2.a.h 1 8.b even 2 1
6336.2.a.k 1 8.d odd 2 1
7744.2.a.b 1 264.p odd 2 1
7744.2.a.bk 1 264.m even 2 1
8624.2.a.c 1 84.h odd 2 1
8712.2.a.x 1 11.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(792))\):

\( T_{5} - 3 \) 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
$5$ \( T - 3 \) Copy content Toggle raw display
$7$ \( T + 2 \) Copy content Toggle raw display
$11$ \( T - 1 \) Copy content Toggle raw display
$13$ \( T \) Copy content Toggle raw display
$17$ \( T - 6 \) Copy content Toggle raw display
$19$ \( T - 4 \) Copy content Toggle raw display
$23$ \( T + 1 \) Copy content Toggle raw display
$29$ \( T - 8 \) Copy content Toggle raw display
$31$ \( T + 7 \) Copy content Toggle raw display
$37$ \( T + 1 \) Copy content Toggle raw display
$41$ \( T + 4 \) Copy content Toggle raw display
$43$ \( T - 6 \) Copy content Toggle raw display
$47$ \( T - 8 \) Copy content Toggle raw display
$53$ \( T + 2 \) Copy content Toggle raw display
$59$ \( T - 1 \) Copy content Toggle raw display
$61$ \( T - 4 \) Copy content Toggle raw display
$67$ \( T + 5 \) Copy content Toggle raw display
$71$ \( T + 3 \) Copy content Toggle raw display
$73$ \( T - 16 \) Copy content Toggle raw display
$79$ \( T - 2 \) Copy content Toggle raw display
$83$ \( T - 2 \) Copy content Toggle raw display
$89$ \( T + 15 \) Copy content Toggle raw display
$97$ \( T + 7 \) Copy content Toggle raw display
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