Properties

Label 7623.2.a.n
Level $7623$
Weight $2$
Character orbit 7623.a
Self dual yes
Analytic conductor $60.870$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7623.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(60.8699614608\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 77)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} - q^{4} + 2 q^{5} + q^{7} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{2} - q^{4} + 2 q^{5} + q^{7} - 3 q^{8} + 2 q^{10} - 4 q^{13} + q^{14} - q^{16} + 4 q^{17} - 2 q^{20} + 4 q^{23} - q^{25} - 4 q^{26} - q^{28} - 6 q^{29} + 10 q^{31} + 5 q^{32} + 4 q^{34} + 2 q^{35} - 6 q^{37} - 6 q^{40} + 4 q^{41} - 12 q^{43} + 4 q^{46} + 10 q^{47} + q^{49} - q^{50} + 4 q^{52} + 6 q^{53} - 3 q^{56} - 6 q^{58} - 2 q^{59} + 10 q^{62} + 7 q^{64} - 8 q^{65} + 8 q^{67} - 4 q^{68} + 2 q^{70} + 12 q^{71} + 8 q^{73} - 6 q^{74} - 8 q^{79} - 2 q^{80} + 4 q^{82} + 8 q^{85} - 12 q^{86} + 6 q^{89} - 4 q^{91} - 4 q^{92} + 10 q^{94} - 10 q^{97} + q^{98}+O(q^{100}) \) 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 1.00000 −3.00000 0 2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(7\) \(-1\)
\(11\) \(-1\)

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 7623.2.a.n 1
3.b odd 2 1 847.2.a.a 1
11.b odd 2 1 693.2.a.a 1
21.c even 2 1 5929.2.a.b 1
33.d even 2 1 77.2.a.c 1
33.f even 10 4 847.2.f.e 4
33.h odd 10 4 847.2.f.k 4
77.b even 2 1 4851.2.a.a 1
132.d odd 2 1 1232.2.a.a 1
165.d even 2 1 1925.2.a.c 1
165.l odd 4 2 1925.2.b.d 2
231.h odd 2 1 539.2.a.d 1
231.k odd 6 2 539.2.e.b 2
231.l even 6 2 539.2.e.a 2
264.m even 2 1 4928.2.a.g 1
264.p odd 2 1 4928.2.a.bi 1
924.n even 2 1 8624.2.a.bc 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
77.2.a.c 1 33.d even 2 1
539.2.a.d 1 231.h odd 2 1
539.2.e.a 2 231.l even 6 2
539.2.e.b 2 231.k odd 6 2
693.2.a.a 1 11.b odd 2 1
847.2.a.a 1 3.b odd 2 1
847.2.f.e 4 33.f even 10 4
847.2.f.k 4 33.h odd 10 4
1232.2.a.a 1 132.d odd 2 1
1925.2.a.c 1 165.d even 2 1
1925.2.b.d 2 165.l odd 4 2
4851.2.a.a 1 77.b even 2 1
4928.2.a.g 1 264.m even 2 1
4928.2.a.bi 1 264.p odd 2 1
5929.2.a.b 1 21.c even 2 1
7623.2.a.n 1 1.a even 1 1 trivial
8624.2.a.bc 1 924.n even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7623))\):

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