Properties

Label 7623.2.a.r
Level 7623
Weight 2
Character orbit 7623.a
Self dual yes
Analytic conductor 60.870
Analytic rank 1
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: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + 2q^{2} + 2q^{4} + q^{5} + q^{7} + O(q^{10}) \) \( q + 2q^{2} + 2q^{4} + q^{5} + q^{7} + 2q^{10} - 4q^{13} + 2q^{14} - 4q^{16} - q^{17} + 2q^{20} - 4q^{23} - 4q^{25} - 8q^{26} + 2q^{28} - 2q^{31} - 8q^{32} - 2q^{34} + q^{35} + 6q^{37} + 2q^{41} - 3q^{43} - 8q^{46} - 7q^{47} + q^{49} - 8q^{50} - 8q^{52} - 12q^{53} + 5q^{59} - 12q^{61} - 4q^{62} - 8q^{64} - 4q^{65} + 5q^{67} - 2q^{68} + 2q^{70} + 6q^{71} + 2q^{73} + 12q^{74} - 8q^{79} - 4q^{80} + 4q^{82} - 15q^{83} - q^{85} - 6q^{86} - 9q^{89} - 4q^{91} - 8q^{92} - 14q^{94} + 2q^{97} + 2q^{98} + O(q^{100}) \)

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
2.00000 0 2.00000 1.00000 0 1.00000 0 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.r yes 1
3.b odd 2 1 7623.2.a.b 1
11.b odd 2 1 7623.2.a.c yes 1
33.d even 2 1 7623.2.a.p yes 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
7623.2.a.b 1 3.b odd 2 1
7623.2.a.c yes 1 11.b odd 2 1
7623.2.a.p yes 1 33.d even 2 1
7623.2.a.r yes 1 1.a even 1 1 trivial

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

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