Properties

Label 4730.2.a.d
Level 4730
Weight 2
Character orbit 4730.a
Self dual yes
Analytic conductor 37.769
Analytic rank 1
Dimension 1
CM no
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4730.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(37.7692401561\)
Analytic rank: \(1\)
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

\(f(q)\) \(=\) \( q + q^{2} - 3q^{3} + q^{4} + q^{5} - 3q^{6} + q^{7} + q^{8} + 6q^{9} + O(q^{10}) \) \( q + q^{2} - 3q^{3} + q^{4} + q^{5} - 3q^{6} + q^{7} + q^{8} + 6q^{9} + q^{10} + q^{11} - 3q^{12} + q^{14} - 3q^{15} + q^{16} - 3q^{17} + 6q^{18} - q^{19} + q^{20} - 3q^{21} + q^{22} - 4q^{23} - 3q^{24} + q^{25} - 9q^{27} + q^{28} - 5q^{29} - 3q^{30} - 3q^{31} + q^{32} - 3q^{33} - 3q^{34} + q^{35} + 6q^{36} - 11q^{37} - q^{38} + q^{40} - 3q^{42} + q^{43} + q^{44} + 6q^{45} - 4q^{46} + 6q^{47} - 3q^{48} - 6q^{49} + q^{50} + 9q^{51} - 9q^{53} - 9q^{54} + q^{55} + q^{56} + 3q^{57} - 5q^{58} + 4q^{59} - 3q^{60} + 13q^{61} - 3q^{62} + 6q^{63} + q^{64} - 3q^{66} + 12q^{67} - 3q^{68} + 12q^{69} + q^{70} + 9q^{71} + 6q^{72} - 10q^{73} - 11q^{74} - 3q^{75} - q^{76} + q^{77} - 4q^{79} + q^{80} + 9q^{81} - 3q^{84} - 3q^{85} + q^{86} + 15q^{87} + q^{88} - q^{89} + 6q^{90} - 4q^{92} + 9q^{93} + 6q^{94} - q^{95} - 3q^{96} - 6q^{98} + 6q^{99} + O(q^{100}) \)

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 −3.00000 1.00000 1.00000 −3.00000 1.00000 1.00000 6.00000 1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

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 4730.2.a.d 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4730.2.a.d 1 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(-1\)
\(11\) \(-1\)
\(43\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4730))\):

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

Hecke Characteristic Polynomials

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