Properties

Label 26.2.a.b
Level 26
Weight 2
Character orbit 26.a
Self dual Yes
Analytic conductor 0.208
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 26 = 2 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 26.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.207611045255\)
Analytic rank: \(0\)
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

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

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 −3.00000 1.00000 −1.00000 −3.00000 1.00000 1.00000 6.00000 −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
\(2\) \(-1\)
\(13\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{3} + 3 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\).