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 $1$

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

$q$-expansion

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

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:

Atkin-Lehner signs

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

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

Hecke kernels

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

\( T_{2} + 2 \) Copy content Toggle raw display
\( T_{5} - 3 \) Copy content Toggle raw display
\( T_{13} - 2 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 2 \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T - 3 \) Copy content Toggle raw display
$7$ \( T + 1 \) Copy content Toggle raw display
$11$ \( T \) Copy content Toggle raw display
$13$ \( T - 2 \) Copy content Toggle raw display
$17$ \( T + 3 \) Copy content Toggle raw display
$19$ \( T + 4 \) Copy content Toggle raw display
$23$ \( T + 2 \) Copy content Toggle raw display
$29$ \( T + 8 \) Copy content Toggle raw display
$31$ \( T - 2 \) Copy content Toggle raw display
$37$ \( T - 10 \) Copy content Toggle raw display
$41$ \( T + 2 \) Copy content Toggle raw display
$43$ \( T - 9 \) Copy content Toggle raw display
$47$ \( T + 9 \) Copy content Toggle raw display
$53$ \( T - 8 \) Copy content Toggle raw display
$59$ \( T - 3 \) Copy content Toggle raw display
$61$ \( T + 10 \) Copy content Toggle raw display
$67$ \( T - 13 \) Copy content Toggle raw display
$71$ \( T + 14 \) Copy content Toggle raw display
$73$ \( T + 10 \) Copy content Toggle raw display
$79$ \( T + 4 \) Copy content Toggle raw display
$83$ \( T + 1 \) Copy content Toggle raw display
$89$ \( T - 9 \) Copy content Toggle raw display
$97$ \( T + 16 \) Copy content Toggle raw display
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