Properties

Label 2016.1.l.a
Level 2016
Weight 1
Character orbit 2016.l
Self dual Yes
Analytic conductor 1.006
Analytic rank 0
Dimension 1
Projective image \(D_{2}\)
CM/RM disc. -7, -56, 8
Inner twists 4

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 2016.l (of order \(2\) and degree \(1\))

Newform invariants

Self dual: Yes
Analytic conductor: \(1.00611506547\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Projective image \(D_{2}\)
Projective field Galois closure of \(\Q(\sqrt{2}, \sqrt{-7})\)
Artin image size \(8\)
Artin image $D_4$
Artin field Galois closure of 4.0.14112.1

$q$-expansion

\(f(q)\) \(=\) \(q \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut q^{7} \) \(\mathstrut +\mathstrut 2q^{23} \) \(\mathstrut -\mathstrut q^{25} \) \(\mathstrut +\mathstrut q^{49} \) \(\mathstrut -\mathstrut 2q^{71} \) \(\mathstrut +\mathstrut 2q^{79} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2016\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(1765\) \(1793\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
433.1
0
0 0 0 0 0 1.00000 0 0 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
7.b Odd 1 CM by \(\Q(\sqrt{-7}) \) yes
8.b Even 1 RM by \(\Q(\sqrt{2}) \) yes
56.h Odd 1 CM by \(\Q(\sqrt{-14}) \) yes

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{11} \) acting on \(S_{1}^{\mathrm{new}}(2016, [\chi])\).