Properties

Label 16.4.a.a
Level 16
Weight 4
Character orbit 16.a
Self dual Yes
Analytic conductor 0.944
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 16.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.944030560092\)
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

\(f(q)\) \(=\) \( q + 4q^{3} - 2q^{5} - 24q^{7} - 11q^{9} + O(q^{10}) \) \( q + 4q^{3} - 2q^{5} - 24q^{7} - 11q^{9} + 44q^{11} + 22q^{13} - 8q^{15} + 50q^{17} - 44q^{19} - 96q^{21} + 56q^{23} - 121q^{25} - 152q^{27} + 198q^{29} + 160q^{31} + 176q^{33} + 48q^{35} - 162q^{37} + 88q^{39} - 198q^{41} - 52q^{43} + 22q^{45} - 528q^{47} + 233q^{49} + 200q^{51} - 242q^{53} - 88q^{55} - 176q^{57} + 668q^{59} + 550q^{61} + 264q^{63} - 44q^{65} - 188q^{67} + 224q^{69} - 728q^{71} + 154q^{73} - 484q^{75} - 1056q^{77} + 656q^{79} - 311q^{81} - 236q^{83} - 100q^{85} + 792q^{87} + 714q^{89} - 528q^{91} + 640q^{93} + 88q^{95} - 478q^{97} - 484q^{99} + O(q^{100}) \)

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 4.00000 0 −2.00000 0 −24.0000 0 −11.0000 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
\(2\) \(1\)

Hecke kernels

There are no other newforms in \(S_{4}^{\mathrm{new}}(\Gamma_0(16))\).