Properties

Label 19.2.a.a
Level 19
Weight 2
Character orbit 19.a
Self dual Yes
Analytic conductor 0.152
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(0.15171576384\)
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

\(f(q)\) \(=\) \( q - 2q^{3} - 2q^{4} + 3q^{5} - q^{7} + q^{9} + O(q^{10}) \) \( q - 2q^{3} - 2q^{4} + 3q^{5} - q^{7} + q^{9} + 3q^{11} + 4q^{12} - 4q^{13} - 6q^{15} + 4q^{16} - 3q^{17} + q^{19} - 6q^{20} + 2q^{21} + 4q^{25} + 4q^{27} + 2q^{28} + 6q^{29} - 4q^{31} - 6q^{33} - 3q^{35} - 2q^{36} + 2q^{37} + 8q^{39} - 6q^{41} - q^{43} - 6q^{44} + 3q^{45} - 3q^{47} - 8q^{48} - 6q^{49} + 6q^{51} + 8q^{52} + 12q^{53} + 9q^{55} - 2q^{57} - 6q^{59} + 12q^{60} - q^{61} - q^{63} - 8q^{64} - 12q^{65} - 4q^{67} + 6q^{68} + 6q^{71} - 7q^{73} - 8q^{75} - 2q^{76} - 3q^{77} + 8q^{79} + 12q^{80} - 11q^{81} + 12q^{83} - 4q^{84} - 9q^{85} - 12q^{87} + 12q^{89} + 4q^{91} + 8q^{93} + 3q^{95} + 8q^{97} + 3q^{99} + O(q^{100}) \)

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
0 −2.00000 −2.00000 3.00000 0 −1.00000 0 1.00000 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
\(19\) \(-1\)

Hecke kernels

There are no other newforms in \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\).