Properties

Label 76.2.a.a
Level 76
Weight 2
Character orbit 76.a
Self dual Yes
Analytic conductor 0.607
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 76.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.606863055362\)
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

\(f(q)\) \(=\) \( q + 2q^{3} - q^{5} - 3q^{7} + q^{9} + O(q^{10}) \) \( q + 2q^{3} - q^{5} - 3q^{7} + q^{9} + 5q^{11} - 4q^{13} - 2q^{15} - 3q^{17} - q^{19} - 6q^{21} + 8q^{23} - 4q^{25} - 4q^{27} - 2q^{29} + 4q^{31} + 10q^{33} + 3q^{35} + 10q^{37} - 8q^{39} + 10q^{41} + q^{43} - q^{45} - q^{47} + 2q^{49} - 6q^{51} - 4q^{53} - 5q^{55} - 2q^{57} + 6q^{59} - 13q^{61} - 3q^{63} + 4q^{65} - 12q^{67} + 16q^{69} + 2q^{71} + 9q^{73} - 8q^{75} - 15q^{77} + 8q^{79} - 11q^{81} - 12q^{83} + 3q^{85} - 4q^{87} + 12q^{89} + 12q^{91} + 8q^{93} + q^{95} - 8q^{97} + 5q^{99} + O(q^{100}) \)

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 0 −1.00000 0 −3.00000 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
\(2\) \(-1\)
\(19\) \(1\)

Hecke kernels

There are no other newforms in \(S_{2}^{\mathrm{new}}(\Gamma_0(76))\).