Properties

Label 6026.2.a.b
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

Downloads

Learn more about

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

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

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 0 1.00000 3.00000 0 −2.00000 −1.00000 −3.00000 −3.00000
\(n\): 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6026))\):

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