Properties

Label 4730.2.a.a
Level 4730
Weight 2
Character orbit 4730.a
Self dual yes
Analytic conductor 37.769
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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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: \(0\)
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

\(f(q)\) \(=\) \( q - q^{2} - 2q^{3} + q^{4} + q^{5} + 2q^{6} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - 2q^{3} + q^{4} + q^{5} + 2q^{6} - q^{8} + q^{9} - q^{10} + q^{11} - 2q^{12} + 2q^{13} - 2q^{15} + q^{16} + 6q^{17} - q^{18} + 6q^{19} + q^{20} - q^{22} + 6q^{23} + 2q^{24} + q^{25} - 2q^{26} + 4q^{27} + 2q^{29} + 2q^{30} - q^{32} - 2q^{33} - 6q^{34} + q^{36} - 2q^{37} - 6q^{38} - 4q^{39} - q^{40} - 6q^{41} + q^{43} + q^{44} + q^{45} - 6q^{46} + 2q^{47} - 2q^{48} - 7q^{49} - q^{50} - 12q^{51} + 2q^{52} + 12q^{53} - 4q^{54} + q^{55} - 12q^{57} - 2q^{58} - 12q^{59} - 2q^{60} + 6q^{61} + q^{64} + 2q^{65} + 2q^{66} - 4q^{67} + 6q^{68} - 12q^{69} + 16q^{71} - q^{72} + 2q^{73} + 2q^{74} - 2q^{75} + 6q^{76} + 4q^{78} + 6q^{79} + q^{80} - 11q^{81} + 6q^{82} - 4q^{83} + 6q^{85} - q^{86} - 4q^{87} - q^{88} - 2q^{89} - q^{90} + 6q^{92} - 2q^{94} + 6q^{95} + 2q^{96} - 2q^{97} + 7q^{98} + q^{99} + O(q^{100}) \)

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 −2.00000 1.00000 1.00000 2.00000 0 −1.00000 1.00000 −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.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4730.2.a.a 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4730))\):

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