Properties

Label 4020.2.a.a
Level 4020
Weight 2
Character orbit 4020.a
Self dual yes
Analytic conductor 32.100
Analytic rank 1
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4020.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.0998616126\)
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

\(f(q)\) \(=\) \( q + q^{3} - q^{5} - 2q^{7} + q^{9} + O(q^{10}) \) \( q + q^{3} - q^{5} - 2q^{7} + q^{9} - 2q^{11} + 2q^{13} - q^{15} + 5q^{17} + q^{19} - 2q^{21} - 3q^{23} + q^{25} + q^{27} - 9q^{29} - 4q^{31} - 2q^{33} + 2q^{35} - 11q^{37} + 2q^{39} + 6q^{41} + 10q^{43} - q^{45} - 5q^{47} - 3q^{49} + 5q^{51} - 12q^{53} + 2q^{55} + q^{57} + 7q^{59} + 8q^{61} - 2q^{63} - 2q^{65} - q^{67} - 3q^{69} + 4q^{71} - 5q^{73} + q^{75} + 4q^{77} + 4q^{79} + q^{81} - 4q^{83} - 5q^{85} - 9q^{87} - 9q^{89} - 4q^{91} - 4q^{93} - q^{95} + 2q^{97} - 2q^{99} + O(q^{100}) \)

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
0 1.00000 0 −1.00000 0 −2.00000 0 1.00000 0
\(n\): 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 4020.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4020.2.a.a 1 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(5\) \(1\)
\(67\) \(1\)

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7} + 2 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4020))\).