Properties

Label 16.3.c.a
Level 16
Weight 3
Character orbit 16.c
Self dual Yes
Analytic conductor 0.436
Analytic rank 0
Dimension 1
CM disc. -4
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 16.c (of order \(2\) and degree \(1\))

Newform invariants

Self dual: Yes
Analytic conductor: \(0.435968422976\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\) \(=\) \(q \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut 10q^{13} \) \(\mathstrut -\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 11q^{25} \) \(\mathstrut +\mathstrut 42q^{29} \) \(\mathstrut -\mathstrut 70q^{37} \) \(\mathstrut +\mathstrut 18q^{41} \) \(\mathstrut -\mathstrut 54q^{45} \) \(\mathstrut +\mathstrut 49q^{49} \) \(\mathstrut +\mathstrut 90q^{53} \) \(\mathstrut -\mathstrut 22q^{61} \) \(\mathstrut -\mathstrut 60q^{65} \) \(\mathstrut -\mathstrut 110q^{73} \) \(\mathstrut +\mathstrut 81q^{81} \) \(\mathstrut +\mathstrut 180q^{85} \) \(\mathstrut -\mathstrut 78q^{89} \) \(\mathstrut +\mathstrut 130q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(1\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
15.1
0
0 0 0 −6.00000 0 0 0 9.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char. orbit Parity Mult. Self Twist Proved
1.a Even 1 trivial yes
4.b Odd 1 CM by \(\Q(\sqrt{-1}) \) yes

Hecke kernels

There are no other newforms in \(S_{3}^{\mathrm{new}}(16, [\chi])\).