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

\(f(q)\) \(=\) \( q + q^{2} - q^{4} + 2q^{5} + q^{7} - 3q^{8} + O(q^{10}) \) \( q + q^{2} - q^{4} + 2q^{5} + q^{7} - 3q^{8} + 2q^{10} - 4q^{13} + q^{14} - q^{16} + 4q^{17} - 2q^{20} + 4q^{23} - q^{25} - 4q^{26} - q^{28} - 6q^{29} + 10q^{31} + 5q^{32} + 4q^{34} + 2q^{35} - 6q^{37} - 6q^{40} + 4q^{41} - 12q^{43} + 4q^{46} + 10q^{47} + q^{49} - q^{50} + 4q^{52} + 6q^{53} - 3q^{56} - 6q^{58} - 2q^{59} + 10q^{62} + 7q^{64} - 8q^{65} + 8q^{67} - 4q^{68} + 2q^{70} + 12q^{71} + 8q^{73} - 6q^{74} - 8q^{79} - 2q^{80} + 4q^{82} + 8q^{85} - 12q^{86} + 6q^{89} - 4q^{91} - 4q^{92} + 10q^{94} - 10q^{97} + q^{98} + O(q^{100}) \)

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
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:

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

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 \(S_{2}^{\mathrm{new}}(\Gamma_0(7623))\):

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