Properties

Label 4026.2.a.f
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

Related objects

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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

\(f(q)\) \(=\) \( q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + 2q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} + 2q^{7} + q^{8} + q^{9} - q^{10} - q^{11} - q^{12} - 3q^{13} + 2q^{14} + q^{15} + q^{16} + 8q^{17} + q^{18} + 4q^{19} - q^{20} - 2q^{21} - q^{22} + 4q^{23} - q^{24} - 4q^{25} - 3q^{26} - q^{27} + 2q^{28} - 9q^{29} + q^{30} - 3q^{31} + q^{32} + q^{33} + 8q^{34} - 2q^{35} + q^{36} + 6q^{37} + 4q^{38} + 3q^{39} - q^{40} + 3q^{41} - 2q^{42} + 4q^{43} - q^{44} - q^{45} + 4q^{46} - q^{48} - 3q^{49} - 4q^{50} - 8q^{51} - 3q^{52} + 8q^{53} - q^{54} + q^{55} + 2q^{56} - 4q^{57} - 9q^{58} - 3q^{59} + q^{60} - q^{61} - 3q^{62} + 2q^{63} + q^{64} + 3q^{65} + q^{66} + 4q^{67} + 8q^{68} - 4q^{69} - 2q^{70} + 6q^{71} + q^{72} + 12q^{73} + 6q^{74} + 4q^{75} + 4q^{76} - 2q^{77} + 3q^{78} - 4q^{79} - q^{80} + q^{81} + 3q^{82} + 4q^{83} - 2q^{84} - 8q^{85} + 4q^{86} + 9q^{87} - q^{88} - 17q^{89} - q^{90} - 6q^{91} + 4q^{92} + 3q^{93} - 4q^{95} - q^{96} + 13q^{97} - 3q^{98} - q^{99} + O(q^{100}) \)

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 −1.00000 −1.00000 2.00000 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 4026.2.a.f 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4026.2.a.f 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(4026))\):

\( T_{5} + 1 \)
\( T_{7} - 2 \)
\( T_{13} + 3 \)