Properties

Label 7623.2.a.d
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

Related objects

Downloads

Learn more about

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: no (minimal twist has level 2541)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 2q^{2} + 2q^{4} + 3q^{5} - q^{7} + O(q^{10}) \) \( q - 2q^{2} + 2q^{4} + 3q^{5} - q^{7} - 6q^{10} + 2q^{13} + 2q^{14} - 4q^{16} - 3q^{17} - 4q^{19} + 6q^{20} - 2q^{23} + 4q^{25} - 4q^{26} - 2q^{28} - 8q^{29} + 2q^{31} + 8q^{32} + 6q^{34} - 3q^{35} + 10q^{37} + 8q^{38} - 2q^{41} + 9q^{43} + 4q^{46} - 9q^{47} + q^{49} - 8q^{50} + 4q^{52} + 8q^{53} + 16q^{58} + 3q^{59} - 10q^{61} - 4q^{62} - 8q^{64} + 6q^{65} + 13q^{67} - 6q^{68} + 6q^{70} - 14q^{71} - 10q^{73} - 20q^{74} - 8q^{76} - 4q^{79} - 12q^{80} + 4q^{82} - q^{83} - 9q^{85} - 18q^{86} + 9q^{89} - 2q^{91} - 4q^{92} + 18q^{94} - 12q^{95} - 16q^{97} - 2q^{98} + O(q^{100}) \)

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 3.00000 0 −1.00000 0 0 −6.00000
\(n\): 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.d 1
3.b odd 2 1 2541.2.a.k yes 1
11.b odd 2 1 7623.2.a.s 1
33.d even 2 1 2541.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2541.2.a.a 1 33.d even 2 1
2541.2.a.k yes 1 3.b odd 2 1
7623.2.a.d 1 1.a even 1 1 trivial
7623.2.a.s 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(7623))\):

\( T_{2} + 2 \)
\( T_{5} - 3 \)
\( T_{13} - 2 \)