Properties

Label 16.6.a.b
Level 16
Weight 6
Character orbit 16.a
Self dual Yes
Analytic conductor 2.566
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 16.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(2.56614111701\)
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

\(f(q)\) \(=\) \(q \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 54q^{5} \) \(\mathstrut +\mathstrut 88q^{7} \) \(\mathstrut -\mathstrut 99q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 54q^{5} \) \(\mathstrut +\mathstrut 88q^{7} \) \(\mathstrut -\mathstrut 99q^{9} \) \(\mathstrut -\mathstrut 540q^{11} \) \(\mathstrut -\mathstrut 418q^{13} \) \(\mathstrut +\mathstrut 648q^{15} \) \(\mathstrut +\mathstrut 594q^{17} \) \(\mathstrut -\mathstrut 836q^{19} \) \(\mathstrut +\mathstrut 1056q^{21} \) \(\mathstrut +\mathstrut 4104q^{23} \) \(\mathstrut -\mathstrut 209q^{25} \) \(\mathstrut -\mathstrut 4104q^{27} \) \(\mathstrut -\mathstrut 594q^{29} \) \(\mathstrut -\mathstrut 4256q^{31} \) \(\mathstrut -\mathstrut 6480q^{33} \) \(\mathstrut +\mathstrut 4752q^{35} \) \(\mathstrut -\mathstrut 298q^{37} \) \(\mathstrut -\mathstrut 5016q^{39} \) \(\mathstrut +\mathstrut 17226q^{41} \) \(\mathstrut +\mathstrut 12100q^{43} \) \(\mathstrut -\mathstrut 5346q^{45} \) \(\mathstrut +\mathstrut 1296q^{47} \) \(\mathstrut -\mathstrut 9063q^{49} \) \(\mathstrut +\mathstrut 7128q^{51} \) \(\mathstrut +\mathstrut 19494q^{53} \) \(\mathstrut -\mathstrut 29160q^{55} \) \(\mathstrut -\mathstrut 10032q^{57} \) \(\mathstrut +\mathstrut 7668q^{59} \) \(\mathstrut -\mathstrut 34738q^{61} \) \(\mathstrut -\mathstrut 8712q^{63} \) \(\mathstrut -\mathstrut 22572q^{65} \) \(\mathstrut -\mathstrut 21812q^{67} \) \(\mathstrut +\mathstrut 49248q^{69} \) \(\mathstrut +\mathstrut 46872q^{71} \) \(\mathstrut +\mathstrut 67562q^{73} \) \(\mathstrut -\mathstrut 2508q^{75} \) \(\mathstrut -\mathstrut 47520q^{77} \) \(\mathstrut +\mathstrut 76912q^{79} \) \(\mathstrut -\mathstrut 25191q^{81} \) \(\mathstrut -\mathstrut 67716q^{83} \) \(\mathstrut +\mathstrut 32076q^{85} \) \(\mathstrut -\mathstrut 7128q^{87} \) \(\mathstrut +\mathstrut 29754q^{89} \) \(\mathstrut -\mathstrut 36784q^{91} \) \(\mathstrut -\mathstrut 51072q^{93} \) \(\mathstrut -\mathstrut 45144q^{95} \) \(\mathstrut -\mathstrut 122398q^{97} \) \(\mathstrut +\mathstrut 53460q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 12.0000 0 54.0000 0 88.0000 0 −99.0000 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

This newform can be constructed as the kernel of the linear operator \(T_{3} \) \(\mathstrut -\mathstrut 12 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(16))\).