Properties

Label 4830.2.a.w
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

\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} - q^{7} + q^{8} + q^{9} + q^{10} - q^{12} + 2q^{13} - q^{14} - q^{15} + q^{16} - 4q^{17} + q^{18} + 8q^{19} + q^{20} + q^{21} + q^{23} - q^{24} + q^{25} + 2q^{26} - q^{27} - q^{28} - q^{30} - 4q^{31} + q^{32} - 4q^{34} - q^{35} + q^{36} + 6q^{37} + 8q^{38} - 2q^{39} + q^{40} - 4q^{41} + q^{42} - 4q^{43} + q^{45} + q^{46} + 12q^{47} - q^{48} + q^{49} + q^{50} + 4q^{51} + 2q^{52} - 4q^{53} - q^{54} - q^{56} - 8q^{57} - q^{60} - 2q^{61} - 4q^{62} - q^{63} + q^{64} + 2q^{65} + 12q^{67} - 4q^{68} - q^{69} - q^{70} - 8q^{71} + q^{72} + 16q^{73} + 6q^{74} - q^{75} + 8q^{76} - 2q^{78} - 4q^{79} + q^{80} + q^{81} - 4q^{82} + q^{84} - 4q^{85} - 4q^{86} + 6q^{89} + q^{90} - 2q^{91} + q^{92} + 4q^{93} + 12q^{94} + 8q^{95} - q^{96} + 2q^{97} + q^{98} + O(q^{100}) \)

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

\( T_{11} \)
\( T_{13} - 2 \)
\( T_{17} + 4 \)
\( T_{19} - 8 \)
\( T_{29} \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -1 + T \)
$3$ \( 1 + T \)
$5$ \( -1 + T \)
$7$ \( 1 + T \)
$11$ \( T \)
$13$ \( -2 + T \)
$17$ \( 4 + T \)
$19$ \( -8 + T \)
$23$ \( -1 + T \)
$29$ \( T \)
$31$ \( 4 + T \)
$37$ \( -6 + T \)
$41$ \( 4 + T \)
$43$ \( 4 + T \)
$47$ \( -12 + T \)
$53$ \( 4 + T \)
$59$ \( T \)
$61$ \( 2 + T \)
$67$ \( -12 + T \)
$71$ \( 8 + T \)
$73$ \( -16 + T \)
$79$ \( 4 + T \)
$83$ \( T \)
$89$ \( -6 + T \)
$97$ \( -2 + T \)
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