Properties

Label 4026.2.a.i
Level 4026
Weight 2
Character orbit 4026.a
Self dual yes
Analytic conductor 32.148
Analytic rank 0
Dimension 1
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4026.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1477718538\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{3} + q^{4} + q^{6} - 4q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} + q^{4} + q^{6} - 4q^{7} + q^{8} + q^{9} - q^{11} + q^{12} + 2q^{13} - 4q^{14} + q^{16} + 6q^{17} + q^{18} - 4q^{19} - 4q^{21} - q^{22} + q^{24} - 5q^{25} + 2q^{26} + q^{27} - 4q^{28} + 6q^{29} + 2q^{31} + q^{32} - q^{33} + 6q^{34} + q^{36} + 8q^{37} - 4q^{38} + 2q^{39} + 12q^{41} - 4q^{42} + 2q^{43} - q^{44} + 6q^{47} + q^{48} + 9q^{49} - 5q^{50} + 6q^{51} + 2q^{52} + 6q^{53} + q^{54} - 4q^{56} - 4q^{57} + 6q^{58} + 12q^{59} + q^{61} + 2q^{62} - 4q^{63} + q^{64} - q^{66} - 4q^{67} + 6q^{68} - 12q^{71} + q^{72} + 2q^{73} + 8q^{74} - 5q^{75} - 4q^{76} + 4q^{77} + 2q^{78} - 4q^{79} + q^{81} + 12q^{82} - 6q^{83} - 4q^{84} + 2q^{86} + 6q^{87} - q^{88} - 6q^{89} - 8q^{91} + 2q^{93} + 6q^{94} + q^{96} + 2q^{97} + 9q^{98} - q^{99} + O(q^{100}) \)

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 1.00000 1.00000 0 1.00000 −4.00000 1.00000 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 4026.2.a.i 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4026.2.a.i 1 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(3\) \(-1\)
\(11\) \(1\)
\(61\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4026))\):

\( T_{5} \)
\( T_{7} + 4 \)
\( T_{13} - 2 \)