Properties

Label 4830.2.a.j
Level $4830$
Weight $2$
Character orbit 4830.a
Self dual yes
Analytic conductor $38.568$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4830.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(38.5677441763\)
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

\(f(q)\) \(=\) \( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{7} - q^{8} + q^{9} + q^{10} + 6q^{11} + q^{12} - 2q^{13} + q^{14} - q^{15} + q^{16} - q^{18} + 6q^{19} - q^{20} - q^{21} - 6q^{22} - q^{23} - q^{24} + q^{25} + 2q^{26} + q^{27} - q^{28} - 4q^{29} + q^{30} + 2q^{31} - q^{32} + 6q^{33} + q^{35} + q^{36} - 6q^{37} - 6q^{38} - 2q^{39} + q^{40} + 6q^{41} + q^{42} + 6q^{43} + 6q^{44} - q^{45} + q^{46} + 2q^{47} + q^{48} + q^{49} - q^{50} - 2q^{52} - 2q^{53} - q^{54} - 6q^{55} + q^{56} + 6q^{57} + 4q^{58} + 4q^{59} - q^{60} - 2q^{61} - 2q^{62} - q^{63} + q^{64} + 2q^{65} - 6q^{66} - 2q^{67} - q^{69} - q^{70} + 10q^{71} - q^{72} - 6q^{73} + 6q^{74} + q^{75} + 6q^{76} - 6q^{77} + 2q^{78} - q^{80} + q^{81} - 6q^{82} - 6q^{83} - q^{84} - 6q^{86} - 4q^{87} - 6q^{88} + 10q^{89} + q^{90} + 2q^{91} - q^{92} + 2q^{93} - 2q^{94} - 6q^{95} - q^{96} - 10q^{97} - q^{98} + 6q^{99} + O(q^{100}) \)

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3\) \(-1\)
\(5\) \(1\)
\(7\) \(1\)
\(23\) \(1\)

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 4830.2.a.j 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4830.2.a.j 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4830))\):

\( T_{11} - 6 \)
\( T_{13} + 2 \)
\( T_{17} \)
\( T_{19} - 6 \)
\( T_{29} + 4 \)

Hecke characteristic polynomials

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