Properties

Label 6026.2.a.d
Level 6026
Weight 2
Character orbit 6026.a
Self dual Yes
Analytic conductor 48.118
Analytic rank 1
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.117852258\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{2} + 2q^{3} + q^{4} - q^{5} + 2q^{6} + 2q^{7} + q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} + 2q^{3} + q^{4} - q^{5} + 2q^{6} + 2q^{7} + q^{8} + q^{9} - q^{10} - 5q^{11} + 2q^{12} - 2q^{13} + 2q^{14} - 2q^{15} + q^{16} - 3q^{17} + q^{18} - 6q^{19} - q^{20} + 4q^{21} - 5q^{22} - q^{23} + 2q^{24} - 4q^{25} - 2q^{26} - 4q^{27} + 2q^{28} - 2q^{29} - 2q^{30} + 4q^{31} + q^{32} - 10q^{33} - 3q^{34} - 2q^{35} + q^{36} + 2q^{37} - 6q^{38} - 4q^{39} - q^{40} + 7q^{41} + 4q^{42} - q^{43} - 5q^{44} - q^{45} - q^{46} - 6q^{47} + 2q^{48} - 3q^{49} - 4q^{50} - 6q^{51} - 2q^{52} + 6q^{53} - 4q^{54} + 5q^{55} + 2q^{56} - 12q^{57} - 2q^{58} + 10q^{59} - 2q^{60} - 3q^{61} + 4q^{62} + 2q^{63} + q^{64} + 2q^{65} - 10q^{66} - 10q^{67} - 3q^{68} - 2q^{69} - 2q^{70} - 2q^{71} + q^{72} - 16q^{73} + 2q^{74} - 8q^{75} - 6q^{76} - 10q^{77} - 4q^{78} + 4q^{79} - q^{80} - 11q^{81} + 7q^{82} - 12q^{83} + 4q^{84} + 3q^{85} - q^{86} - 4q^{87} - 5q^{88} - 16q^{89} - q^{90} - 4q^{91} - q^{92} + 8q^{93} - 6q^{94} + 6q^{95} + 2q^{96} + 10q^{97} - 3q^{98} - 5q^{99} + O(q^{100}) \)

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 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.

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(23\) \(1\)
\(131\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\):

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