Properties

Label 126.2.a.b
Level 126
Weight 2
Character orbit 126.a
Self dual Yes
Analytic conductor 1.006
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 126.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.00611506547\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{4} + q^{7} + q^{8} + O(q^{10}) \) \( q + q^{2} + q^{4} + q^{7} + q^{8} - 4q^{13} + q^{14} + q^{16} - 6q^{17} + 2q^{19} - 5q^{25} - 4q^{26} + q^{28} + 6q^{29} - 4q^{31} + q^{32} - 6q^{34} + 2q^{37} + 2q^{38} - 6q^{41} + 8q^{43} + 12q^{47} + q^{49} - 5q^{50} - 4q^{52} - 6q^{53} + q^{56} + 6q^{58} + 6q^{59} + 8q^{61} - 4q^{62} + q^{64} - 4q^{67} - 6q^{68} + 2q^{73} + 2q^{74} + 2q^{76} + 8q^{79} - 6q^{82} + 6q^{83} + 8q^{86} + 6q^{89} - 4q^{91} + 12q^{94} - 10q^{97} + q^{98} + O(q^{100}) \)

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 0 0 1.00000 1.00000 0 0
\(n\): 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
\(2\) \(-1\)
\(3\) \(-1\)
\(7\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{5} \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(126))\).