Properties

Label 54.2.a.a
Level 54
Weight 2
Character orbit 54.a
Self dual Yes
Analytic conductor 0.431
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 54.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.431192170915\)
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

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

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 3.00000 0 −1.00000 −1.00000 0 −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
\(2\) \(1\)
\(3\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{5} - 3 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(54))\).