Properties

Label 4028.2.a.a
Level 4028
Weight 2
Character orbit 4028.a
Self dual yes
Analytic conductor 32.164
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1637419342\)
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

\(f(q)\) \(=\) \( q + q^{3} + 4q^{7} - 2q^{9} + O(q^{10}) \) \( q + q^{3} + 4q^{7} - 2q^{9} + q^{11} - 6q^{13} + 3q^{17} + q^{19} + 4q^{21} - 6q^{23} - 5q^{25} - 5q^{27} + 4q^{29} + 9q^{31} + q^{33} + 10q^{37} - 6q^{39} + 10q^{41} + 5q^{43} + 8q^{47} + 9q^{49} + 3q^{51} + q^{53} + q^{57} + 12q^{59} + 12q^{61} - 8q^{63} - q^{67} - 6q^{69} - 15q^{71} + 6q^{73} - 5q^{75} + 4q^{77} - 4q^{79} + q^{81} - 6q^{83} + 4q^{87} + 8q^{89} - 24q^{91} + 9q^{93} + 10q^{97} - 2q^{99} + O(q^{100}) \)

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 0 0 4.00000 0 −2.00000 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 4028.2.a.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4028.2.a.a 1 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(19\) \(-1\)
\(53\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4028))\):

\( T_{3} - 1 \)
\( T_{5} \)