Properties

Label 7623.2.a.a
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 2541)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2q^{2} + 2q^{4} - q^{5} + q^{7} + O(q^{10}) \) \( q - 2q^{2} + 2q^{4} - q^{5} + q^{7} + 2q^{10} - 6q^{13} - 2q^{14} - 4q^{16} + 7q^{17} - 8q^{19} - 2q^{20} - 6q^{23} - 4q^{25} + 12q^{26} + 2q^{28} - 4q^{29} + 2q^{31} + 8q^{32} - 14q^{34} - q^{35} - 6q^{37} + 16q^{38} + 2q^{41} - q^{43} + 12q^{46} - 13q^{47} + q^{49} + 8q^{50} - 12q^{52} + 8q^{58} - q^{59} - 10q^{61} - 4q^{62} - 8q^{64} + 6q^{65} - 3q^{67} + 14q^{68} + 2q^{70} + 6q^{71} + 14q^{73} + 12q^{74} - 16q^{76} + 4q^{79} + 4q^{80} - 4q^{82} + 5q^{83} - 7q^{85} + 2q^{86} - 3q^{89} - 6q^{91} - 12q^{92} + 26q^{94} + 8q^{95} - 4q^{97} - 2q^{98} + O(q^{100}) \)

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.a 1
3.b odd 2 1 2541.2.a.l yes 1
11.b odd 2 1 7623.2.a.q 1
33.d even 2 1 2541.2.a.b 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2541.2.a.b 1 33.d even 2 1
2541.2.a.l yes 1 3.b odd 2 1
7623.2.a.a 1 1.a even 1 1 trivial
7623.2.a.q 1 11.b odd 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(7623))\):

\( T_{2} + 2 \)
\( T_{5} + 1 \)
\( T_{13} + 6 \)