Properties

Label 5054.2.a.a
Level $5054$
Weight $2$
Character orbit 5054.a
Self dual yes
Analytic conductor $40.356$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5054.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(40.3563931816\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 266)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - 3 q^{9} - q^{10} - 2 q^{11} + 5 q^{13} - q^{14} + q^{16} + 3 q^{18} + q^{20} + 2 q^{22} + q^{23} - 4 q^{25} - 5 q^{26} + q^{28} - 6 q^{29} - 4 q^{31} - q^{32} + q^{35} - 3 q^{36} + 4 q^{37} - q^{40} + 2 q^{41} - 8 q^{43} - 2 q^{44} - 3 q^{45} - q^{46} + q^{49} + 4 q^{50} + 5 q^{52} + 2 q^{53} - 2 q^{55} - q^{56} + 6 q^{58} + 7 q^{59} - 7 q^{61} + 4 q^{62} - 3 q^{63} + q^{64} + 5 q^{65} - 12 q^{67} - q^{70} + 15 q^{71} + 3 q^{72} - 14 q^{73} - 4 q^{74} - 2 q^{77} + 4 q^{79} + q^{80} + 9 q^{81} - 2 q^{82} - 7 q^{83} + 8 q^{86} + 2 q^{88} + 3 q^{90} + 5 q^{91} + q^{92} - 12 q^{97} - q^{98} + 6 q^{99}+O(q^{100}) \) 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
−1.00000 0 1.00000 1.00000 0 1.00000 −1.00000 −3.00000 −1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(7\) \(-1\)
\(19\) \(-1\)

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 5054.2.a.a 1
19.b odd 2 1 5054.2.a.b 1
19.d odd 6 2 266.2.f.a 2
57.f even 6 2 2394.2.o.i 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
266.2.f.a 2 19.d odd 6 2
2394.2.o.i 2 57.f even 6 2
5054.2.a.a 1 1.a even 1 1 trivial
5054.2.a.b 1 19.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(5054))\):

\( T_{3} \) Copy content Toggle raw display
\( T_{5} - 1 \) Copy content Toggle raw display
\( T_{13} - 5 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 1 \) Copy content Toggle raw display
$3$ \( T \) Copy content Toggle raw display
$5$ \( T - 1 \) Copy content Toggle raw display
$7$ \( T - 1 \) Copy content Toggle raw display
$11$ \( T + 2 \) Copy content Toggle raw display
$13$ \( T - 5 \) Copy content Toggle raw display
$17$ \( T \) Copy content Toggle raw display
$19$ \( T \) Copy content Toggle raw display
$23$ \( T - 1 \) Copy content Toggle raw display
$29$ \( T + 6 \) Copy content Toggle raw display
$31$ \( T + 4 \) Copy content Toggle raw display
$37$ \( T - 4 \) Copy content Toggle raw display
$41$ \( T - 2 \) Copy content Toggle raw display
$43$ \( T + 8 \) Copy content Toggle raw display
$47$ \( T \) Copy content Toggle raw display
$53$ \( T - 2 \) Copy content Toggle raw display
$59$ \( T - 7 \) Copy content Toggle raw display
$61$ \( T + 7 \) Copy content Toggle raw display
$67$ \( T + 12 \) Copy content Toggle raw display
$71$ \( T - 15 \) Copy content Toggle raw display
$73$ \( T + 14 \) Copy content Toggle raw display
$79$ \( T - 4 \) Copy content Toggle raw display
$83$ \( T + 7 \) Copy content Toggle raw display
$89$ \( T \) Copy content Toggle raw display
$97$ \( T + 12 \) Copy content Toggle raw display
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