Properties

Label 4730.2.a.e
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

\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - 2q^{7} + q^{8} - 2q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - 2q^{7} + q^{8} - 2q^{9} - q^{10} + q^{11} - q^{12} + 4q^{13} - 2q^{14} + q^{15} + q^{16} - 2q^{18} - 2q^{19} - q^{20} + 2q^{21} + q^{22} - 2q^{23} - q^{24} + q^{25} + 4q^{26} + 5q^{27} - 2q^{28} + 3q^{29} + q^{30} + 4q^{31} + q^{32} - q^{33} + 2q^{35} - 2q^{36} - 4q^{37} - 2q^{38} - 4q^{39} - q^{40} + 8q^{41} + 2q^{42} - q^{43} + q^{44} + 2q^{45} - 2q^{46} - 2q^{47} - q^{48} - 3q^{49} + q^{50} + 4q^{52} - 9q^{53} + 5q^{54} - q^{55} - 2q^{56} + 2q^{57} + 3q^{58} - 8q^{59} + q^{60} - 13q^{61} + 4q^{62} + 4q^{63} + q^{64} - 4q^{65} - q^{66} + 14q^{67} + 2q^{69} + 2q^{70} - 4q^{71} - 2q^{72} - 13q^{73} - 4q^{74} - q^{75} - 2q^{76} - 2q^{77} - 4q^{78} - 13q^{79} - q^{80} + q^{81} + 8q^{82} + 9q^{83} + 2q^{84} - q^{86} - 3q^{87} + q^{88} - 8q^{89} + 2q^{90} - 8q^{91} - 2q^{92} - 4q^{93} - 2q^{94} + 2q^{95} - q^{96} + 3q^{97} - 3q^{98} - 2q^{99} + O(q^{100}) \)

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 −2.00000 1.00000 −2.00000 −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.e 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4730.2.a.e 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4730))\):

\( T_{3} + 1 \)
\( T_{7} + 2 \)
\( T_{13} - 4 \)