Properties

Label 483.2.a.b
Level $483$
Weight $2$
Character orbit 483.a
Self dual yes
Analytic conductor $3.857$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(3.85677441763\)
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

\(f(q)\) \(=\) \( q + 2q^{2} + q^{3} + 2q^{4} + 4q^{5} + 2q^{6} - q^{7} + q^{9} + O(q^{10}) \) \( q + 2q^{2} + q^{3} + 2q^{4} + 4q^{5} + 2q^{6} - q^{7} + q^{9} + 8q^{10} - 5q^{11} + 2q^{12} - 2q^{13} - 2q^{14} + 4q^{15} - 4q^{16} + 2q^{18} - 5q^{19} + 8q^{20} - q^{21} - 10q^{22} - q^{23} + 11q^{25} - 4q^{26} + q^{27} - 2q^{28} - 2q^{29} + 8q^{30} + 6q^{31} - 8q^{32} - 5q^{33} - 4q^{35} + 2q^{36} + 6q^{37} - 10q^{38} - 2q^{39} + 5q^{41} - 2q^{42} + 8q^{43} - 10q^{44} + 4q^{45} - 2q^{46} - 9q^{47} - 4q^{48} + q^{49} + 22q^{50} - 4q^{52} + 9q^{53} + 2q^{54} - 20q^{55} - 5q^{57} - 4q^{58} + 9q^{59} + 8q^{60} - 5q^{61} + 12q^{62} - q^{63} - 8q^{64} - 8q^{65} - 10q^{66} + 4q^{67} - q^{69} - 8q^{70} + 12q^{71} + 12q^{74} + 11q^{75} - 10q^{76} + 5q^{77} - 4q^{78} - 10q^{79} - 16q^{80} + q^{81} + 10q^{82} - 18q^{83} - 2q^{84} + 16q^{86} - 2q^{87} + 10q^{89} + 8q^{90} + 2q^{91} - 2q^{92} + 6q^{93} - 18q^{94} - 20q^{95} - 8q^{96} - 18q^{97} + 2q^{98} - 5q^{99} + O(q^{100}) \)

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
2.00000 1.00000 2.00000 4.00000 2.00000 −1.00000 0 1.00000 8.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 483.2.a.b 1
3.b odd 2 1 1449.2.a.a 1
4.b odd 2 1 7728.2.a.l 1
7.b odd 2 1 3381.2.a.l 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
483.2.a.b 1 1.a even 1 1 trivial
1449.2.a.a 1 3.b odd 2 1
3381.2.a.l 1 7.b odd 2 1
7728.2.a.l 1 4.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(483))\):

\( T_{2} - 2 \)
\( T_{5} - 4 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -2 + T \)
$3$ \( -1 + T \)
$5$ \( -4 + T \)
$7$ \( 1 + T \)
$11$ \( 5 + T \)
$13$ \( 2 + T \)
$17$ \( T \)
$19$ \( 5 + T \)
$23$ \( 1 + T \)
$29$ \( 2 + T \)
$31$ \( -6 + T \)
$37$ \( -6 + T \)
$41$ \( -5 + T \)
$43$ \( -8 + T \)
$47$ \( 9 + T \)
$53$ \( -9 + T \)
$59$ \( -9 + T \)
$61$ \( 5 + T \)
$67$ \( -4 + T \)
$71$ \( -12 + T \)
$73$ \( T \)
$79$ \( 10 + T \)
$83$ \( 18 + T \)
$89$ \( -10 + T \)
$97$ \( 18 + T \)
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