Properties

Label 62.2.a.a
Level 62
Weight 2
Character orbit 62.a
Self dual Yes
Analytic conductor 0.495
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 62 = 2 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 62.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.495072492532\)
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

\(f(q)\) \(=\) \( q + q^{2} + q^{4} - 2q^{5} + q^{8} - 3q^{9} + O(q^{10}) \) \( q + q^{2} + q^{4} - 2q^{5} + q^{8} - 3q^{9} - 2q^{10} + 2q^{13} + q^{16} - 6q^{17} - 3q^{18} + 4q^{19} - 2q^{20} + 8q^{23} - q^{25} + 2q^{26} + 2q^{29} - q^{31} + q^{32} - 6q^{34} - 3q^{36} + 10q^{37} + 4q^{38} - 2q^{40} - 6q^{41} + 8q^{43} + 6q^{45} + 8q^{46} - 8q^{47} - 7q^{49} - q^{50} + 2q^{52} - 6q^{53} + 2q^{58} - 12q^{59} - 6q^{61} - q^{62} + q^{64} - 4q^{65} - 12q^{67} - 6q^{68} + 8q^{71} - 3q^{72} + 10q^{73} + 10q^{74} + 4q^{76} - 8q^{79} - 2q^{80} + 9q^{81} - 6q^{82} + 8q^{83} + 12q^{85} + 8q^{86} - 6q^{89} + 6q^{90} + 8q^{92} - 8q^{94} - 8q^{95} + 2q^{97} - 7q^{98} + O(q^{100}) \)

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 0 1.00000 −2.00000 0 0 1.00000 −3.00000 −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
\(2\) \(-1\)
\(31\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{3} \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(62))\).