Properties

Label 786.2.a.d
Level 786
Weight 2
Character orbit 786.a
Self dual Yes
Analytic conductor 6.276
Analytic rank 0
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 786 = 2 \cdot 3 \cdot 131 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 786.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(6.27624159887\)
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

\(f(q)\) \(=\) \( q - q^{2} - q^{3} + q^{4} + 2q^{5} + q^{6} - q^{8} + q^{9} + O(q^{10}) \) \( q - q^{2} - q^{3} + q^{4} + 2q^{5} + q^{6} - q^{8} + q^{9} - 2q^{10} + 4q^{11} - q^{12} - 2q^{13} - 2q^{15} + q^{16} - 2q^{17} - q^{18} + 8q^{19} + 2q^{20} - 4q^{22} + q^{24} - q^{25} + 2q^{26} - q^{27} + 2q^{29} + 2q^{30} - 8q^{31} - q^{32} - 4q^{33} + 2q^{34} + q^{36} + 2q^{37} - 8q^{38} + 2q^{39} - 2q^{40} + 10q^{41} - 4q^{43} + 4q^{44} + 2q^{45} + 8q^{47} - q^{48} - 7q^{49} + q^{50} + 2q^{51} - 2q^{52} + 10q^{53} + q^{54} + 8q^{55} - 8q^{57} - 2q^{58} + 12q^{59} - 2q^{60} + 6q^{61} + 8q^{62} + q^{64} - 4q^{65} + 4q^{66} - 2q^{68} + 8q^{71} - q^{72} - 14q^{73} - 2q^{74} + q^{75} + 8q^{76} - 2q^{78} + 16q^{79} + 2q^{80} + q^{81} - 10q^{82} + 12q^{83} - 4q^{85} + 4q^{86} - 2q^{87} - 4q^{88} - 14q^{89} - 2q^{90} + 8q^{93} - 8q^{94} + 16q^{95} + q^{96} + 2q^{97} + 7q^{98} + 4q^{99} + O(q^{100}) \)

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
−1.00000 −1.00000 1.00000 2.00000 1.00000 0 −1.00000 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
\(2\) \(1\)
\(3\) \(1\)
\(131\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(786))\):

\( T_{5} - 2 \)
\( T_{7} \)
\( T_{17} + 2 \)