Properties

Label 4719.2.a.k
Level $4719$
Weight $2$
Character orbit 4719.a
Self dual yes
Analytic conductor $37.681$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4719 = 3 \cdot 11^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4719.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.6814047138\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 429)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + q^{3} - q^{4} - 2q^{5} + q^{6} - 3q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} - q^{4} - 2q^{5} + q^{6} - 3q^{8} + q^{9} - 2q^{10} - q^{12} - q^{13} - 2q^{15} - q^{16} + 6q^{17} + q^{18} + 4q^{19} + 2q^{20} - 8q^{23} - 3q^{24} - q^{25} - q^{26} + q^{27} + 10q^{29} - 2q^{30} + 5q^{32} + 6q^{34} - q^{36} + 6q^{37} + 4q^{38} - q^{39} + 6q^{40} - 10q^{41} - 4q^{43} - 2q^{45} - 8q^{46} + 8q^{47} - q^{48} - 7q^{49} - q^{50} + 6q^{51} + q^{52} - 10q^{53} + q^{54} + 4q^{57} + 10q^{58} - 12q^{59} + 2q^{60} - 14q^{61} + 7q^{64} + 2q^{65} - 12q^{67} - 6q^{68} - 8q^{69} - 3q^{72} + 6q^{73} + 6q^{74} - q^{75} - 4q^{76} - q^{78} - 8q^{79} + 2q^{80} + q^{81} - 10q^{82} - 12q^{83} - 12q^{85} - 4q^{86} + 10q^{87} + 2q^{89} - 2q^{90} + 8q^{92} + 8q^{94} - 8q^{95} + 5q^{96} - 14q^{97} - 7q^{98} + O(q^{100}) \)

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
1.00000 1.00000 −1.00000 −2.00000 1.00000 0 −3.00000 1.00000 −2.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(11\) \(-1\)
\(13\) \(1\)

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 4719.2.a.k 1
11.b odd 2 1 429.2.a.b 1
33.d even 2 1 1287.2.a.e 1
44.c even 2 1 6864.2.a.e 1
143.d odd 2 1 5577.2.a.g 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
429.2.a.b 1 11.b odd 2 1
1287.2.a.e 1 33.d even 2 1
4719.2.a.k 1 1.a even 1 1 trivial
5577.2.a.g 1 143.d odd 2 1
6864.2.a.e 1 44.c even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4719))\):

\( T_{2} - 1 \)
\( T_{5} + 2 \)
\( T_{7} \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( -1 + T \)
$5$ \( 2 + T \)
$7$ \( T \)
$11$ \( T \)
$13$ \( 1 + T \)
$17$ \( -6 + T \)
$19$ \( -4 + T \)
$23$ \( 8 + T \)
$29$ \( -10 + T \)
$31$ \( T \)
$37$ \( -6 + T \)
$41$ \( 10 + T \)
$43$ \( 4 + T \)
$47$ \( -8 + T \)
$53$ \( 10 + T \)
$59$ \( 12 + T \)
$61$ \( 14 + T \)
$67$ \( 12 + T \)
$71$ \( T \)
$73$ \( -6 + T \)
$79$ \( 8 + T \)
$83$ \( 12 + T \)
$89$ \( -2 + T \)
$97$ \( 14 + T \)
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