Properties

Label 162.2.a.b
Level 162
Weight 2
Character orbit 162.a
Self dual Yes
Analytic conductor 1.294
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 162 = 2 \cdot 3^{4} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 162.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(1.29357651274\)
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

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

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 2.00000 −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
\(2\) \(1\)
\(3\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(162))\):

\( T_{5} \)
\( T_{11} - 3 \)