Properties

Label 7623.2.a.j
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

\(f(q)\) \(=\) \( q - 2q^{4} + q^{5} + q^{7} + O(q^{10}) \) \( q - 2q^{4} + q^{5} + q^{7} + 4q^{13} + 4q^{16} + 2q^{17} + 6q^{19} - 2q^{20} + 5q^{23} - 4q^{25} - 2q^{28} + 10q^{29} + q^{31} + q^{35} - 5q^{37} - 2q^{41} + 8q^{43} - 8q^{47} + q^{49} - 8q^{52} + 6q^{53} - 3q^{59} + 2q^{61} - 8q^{64} + 4q^{65} - 3q^{67} - 4q^{68} - q^{71} - 10q^{73} - 12q^{76} - 6q^{79} + 4q^{80} + 12q^{83} + 2q^{85} + 15q^{89} + 4q^{91} - 10q^{92} + 6q^{95} - 5q^{97} + O(q^{100}) \)

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
0 0 −2.00000 1.00000 0 1.00000 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

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

Atkin-Lehner signs

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

Hecke kernels

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

\( T_{2} \)
\( T_{5} - 1 \)
\( T_{13} - 4 \)