Properties

Label 57.2.a.c
Level 57
Weight 2
Character orbit 57.a
Self dual Yes
Analytic conductor 0.455
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

Level: \( N \) = \( 57 = 3 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 57.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.455147291521\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{3} - q^{4} - 2q^{5} + q^{6} - 3q^{8} + q^{9} + O(q^{10}) \) \( q + q^{2} + q^{3} - q^{4} - 2q^{5} + q^{6} - 3q^{8} + q^{9} - 2q^{10} - q^{12} + 6q^{13} - 2q^{15} - q^{16} - 6q^{17} + q^{18} - q^{19} + 2q^{20} + 4q^{23} - 3q^{24} - q^{25} + 6q^{26} + q^{27} + 2q^{29} - 2q^{30} + 8q^{31} + 5q^{32} - 6q^{34} - q^{36} - 10q^{37} - q^{38} + 6q^{39} + 6q^{40} - 2q^{41} - 4q^{43} - 2q^{45} + 4q^{46} + 12q^{47} - q^{48} - 7q^{49} - q^{50} - 6q^{51} - 6q^{52} - 6q^{53} + q^{54} - q^{57} + 2q^{58} - 12q^{59} + 2q^{60} - 2q^{61} + 8q^{62} + 7q^{64} - 12q^{65} - 4q^{67} + 6q^{68} + 4q^{69} - 3q^{72} + 10q^{73} - 10q^{74} - q^{75} + q^{76} + 6q^{78} + 2q^{80} + q^{81} - 2q^{82} + 16q^{83} + 12q^{85} - 4q^{86} + 2q^{87} - 2q^{89} - 2q^{90} - 4q^{92} + 8q^{93} + 12q^{94} + 2q^{95} + 5q^{96} + 10q^{97} - 7q^{98} + O(q^{100}) \)

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 1.00000 −1.00000 −2.00000 1.00000 0 −3.00000 1.00000 −2.00000
\(n\): 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
\(3\) \(-1\)
\(19\) \(1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(57))\):

\( T_{2} - 1 \)
\( T_{5} + 2 \)