Properties

Label 63.2.a.a
Level 63
Weight 2
Character orbit 63.a
Self dual Yes
Analytic conductor 0.503
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 63.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.503057532734\)
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

\(f(q)\) \(=\) \( q + q^{2} - q^{4} + 2q^{5} - q^{7} - 3q^{8} + O(q^{10}) \) \( q + q^{2} - q^{4} + 2q^{5} - q^{7} - 3q^{8} + 2q^{10} - 4q^{11} - 2q^{13} - q^{14} - q^{16} + 6q^{17} + 4q^{19} - 2q^{20} - 4q^{22} - q^{25} - 2q^{26} + q^{28} + 2q^{29} + 5q^{32} + 6q^{34} - 2q^{35} + 6q^{37} + 4q^{38} - 6q^{40} - 2q^{41} - 4q^{43} + 4q^{44} + q^{49} - q^{50} + 2q^{52} - 6q^{53} - 8q^{55} + 3q^{56} + 2q^{58} - 12q^{59} - 2q^{61} + 7q^{64} - 4q^{65} + 4q^{67} - 6q^{68} - 2q^{70} - 6q^{73} + 6q^{74} - 4q^{76} + 4q^{77} - 16q^{79} - 2q^{80} - 2q^{82} + 12q^{83} + 12q^{85} - 4q^{86} + 12q^{88} + 14q^{89} + 2q^{91} + 8q^{95} + 18q^{97} + q^{98} + O(q^{100}) \)

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 2.00000 0 −1.00000 −3.00000 0 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
\(3\) \(-1\)
\(7\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \( T_{2} - 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(63))\).