Properties

Label 4598.2.a.g
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

\(f(q)\) \(=\) \( q - q^{2} + q^{4} + 4q^{5} - q^{7} - q^{8} - 3q^{9} + O(q^{10}) \) \( q - q^{2} + q^{4} + 4q^{5} - q^{7} - q^{8} - 3q^{9} - 4q^{10} - 5q^{13} + q^{14} + q^{16} - 3q^{17} + 3q^{18} - q^{19} + 4q^{20} + 9q^{23} + 11q^{25} + 5q^{26} - q^{28} + 2q^{29} - 10q^{31} - q^{32} + 3q^{34} - 4q^{35} - 3q^{36} - 9q^{37} + q^{38} - 4q^{40} + 2q^{41} + 8q^{43} - 12q^{45} - 9q^{46} + 9q^{47} - 6q^{49} - 11q^{50} - 5q^{52} + 6q^{53} + q^{56} - 2q^{58} + 7q^{59} + 12q^{61} + 10q^{62} + 3q^{63} + q^{64} - 20q^{65} - 3q^{67} - 3q^{68} + 4q^{70} + 12q^{71} + 3q^{72} + 15q^{73} + 9q^{74} - q^{76} + 2q^{79} + 4q^{80} + 9q^{81} - 2q^{82} + 8q^{83} - 12q^{85} - 8q^{86} + 14q^{89} + 12q^{90} + 5q^{91} + 9q^{92} - 9q^{94} - 4q^{95} + 2q^{97} + 6q^{98} + O(q^{100}) \)

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 0 1.00000 4.00000 0 −1.00000 −1.00000 −3.00000 −4.00000
\(n\): 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.g 1
11.b odd 2 1 4598.2.a.o yes 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4598.2.a.g 1 1.a even 1 1 trivial
4598.2.a.o yes 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4598))\):

\( T_{3} \)
\( T_{5} - 4 \)
\( T_{7} + 1 \)
\( T_{13} + 5 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 + T \)
$3$ \( T \)
$5$ \( -4 + T \)
$7$ \( 1 + T \)
$11$ \( T \)
$13$ \( 5 + T \)
$17$ \( 3 + T \)
$19$ \( 1 + T \)
$23$ \( -9 + T \)
$29$ \( -2 + T \)
$31$ \( 10 + T \)
$37$ \( 9 + T \)
$41$ \( -2 + T \)
$43$ \( -8 + T \)
$47$ \( -9 + T \)
$53$ \( -6 + T \)
$59$ \( -7 + T \)
$61$ \( -12 + T \)
$67$ \( 3 + T \)
$71$ \( -12 + T \)
$73$ \( -15 + T \)
$79$ \( -2 + T \)
$83$ \( -8 + T \)
$89$ \( -14 + T \)
$97$ \( -2 + T \)
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