Properties

Label 4830.2.a.e
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

\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{7} - q^{8} + q^{9} - q^{10} + 2q^{11} - q^{12} + 4q^{13} + q^{14} - q^{15} + q^{16} + 6q^{17} - q^{18} - 4q^{19} + q^{20} + q^{21} - 2q^{22} - q^{23} + q^{24} + q^{25} - 4q^{26} - q^{27} - q^{28} + 2q^{29} + q^{30} + 2q^{31} - q^{32} - 2q^{33} - 6q^{34} - q^{35} + q^{36} + 8q^{37} + 4q^{38} - 4q^{39} - q^{40} + 6q^{41} - q^{42} + 2q^{44} + q^{45} + q^{46} + 8q^{47} - q^{48} + q^{49} - q^{50} - 6q^{51} + 4q^{52} - 8q^{53} + q^{54} + 2q^{55} + q^{56} + 4q^{57} - 2q^{58} - 14q^{59} - q^{60} - 6q^{61} - 2q^{62} - q^{63} + q^{64} + 4q^{65} + 2q^{66} - 4q^{67} + 6q^{68} + q^{69} + q^{70} + 4q^{71} - q^{72} + 8q^{73} - 8q^{74} - q^{75} - 4q^{76} - 2q^{77} + 4q^{78} + 10q^{79} + q^{80} + q^{81} - 6q^{82} - 4q^{83} + q^{84} + 6q^{85} - 2q^{87} - 2q^{88} + 6q^{89} - q^{90} - 4q^{91} - q^{92} - 2q^{93} - 8q^{94} - 4q^{95} + q^{96} - 2q^{97} - q^{98} + 2q^{99} + O(q^{100}) \)

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

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

Hecke characteristic polynomials

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