Properties

Label 4598.2.a.s
Level $4598$
Weight $2$
Character orbit 4598.a
Self dual yes
Analytic conductor $36.715$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4598.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7152148494\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + 3q^{3} + q^{4} + 3q^{6} + q^{8} + 6q^{9} + O(q^{10}) \) \( q + q^{2} + 3q^{3} + q^{4} + 3q^{6} + q^{8} + 6q^{9} + 3q^{12} + 7q^{13} + q^{16} - 7q^{17} + 6q^{18} + q^{19} + 8q^{23} + 3q^{24} - 5q^{25} + 7q^{26} + 9q^{27} - 9q^{29} + 2q^{31} + q^{32} - 7q^{34} + 6q^{36} + 3q^{37} + q^{38} + 21q^{39} + 10q^{41} - 10q^{43} + 8q^{46} + 3q^{47} + 3q^{48} - 7q^{49} - 5q^{50} - 21q^{51} + 7q^{52} + 5q^{53} + 9q^{54} + 3q^{57} - 9q^{58} + 4q^{59} + 6q^{61} + 2q^{62} + q^{64} - 3q^{67} - 7q^{68} + 24q^{69} + 2q^{71} + 6q^{72} + 3q^{73} + 3q^{74} - 15q^{75} + q^{76} + 21q^{78} - 14q^{79} + 9q^{81} + 10q^{82} + 6q^{83} - 10q^{86} - 27q^{87} + 6q^{89} + 8q^{92} + 6q^{93} + 3q^{94} + 3q^{96} + 14q^{97} - 7q^{98} + O(q^{100}) \)

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 3.00000 1.00000 0 3.00000 0 1.00000 6.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(11\) \(-1\)
\(19\) \(-1\)

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 4598.2.a.s yes 1
11.b odd 2 1 4598.2.a.k 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4598.2.a.k 1 11.b odd 2 1
4598.2.a.s yes 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4598))\):

\( T_{3} - 3 \)
\( T_{5} \)
\( T_{7} \)
\( T_{13} - 7 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( -3 + T \)
$5$ \( T \)
$7$ \( T \)
$11$ \( T \)
$13$ \( -7 + T \)
$17$ \( 7 + T \)
$19$ \( -1 + T \)
$23$ \( -8 + T \)
$29$ \( 9 + T \)
$31$ \( -2 + T \)
$37$ \( -3 + T \)
$41$ \( -10 + T \)
$43$ \( 10 + T \)
$47$ \( -3 + T \)
$53$ \( -5 + T \)
$59$ \( -4 + T \)
$61$ \( -6 + T \)
$67$ \( 3 + T \)
$71$ \( -2 + T \)
$73$ \( -3 + T \)
$79$ \( 14 + T \)
$83$ \( -6 + T \)
$89$ \( -6 + T \)
$97$ \( -14 + T \)
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