Properties

Label 83.1.b.a
Level 83
Weight 1
Character orbit 83.b
Self dual Yes
Analytic conductor 0.041
Analytic rank 0
Dimension 1
Projective image \(D_{3}\)
CM disc. -83
Inner twists 2

Related objects

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Newspace parameters

Level: \( N \) = \( 83 \)
Weight: \( k \) = \( 1 \)
Character orbit: \([\chi]\) = 83.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: Yes
Analytic conductor: \(0.0414223960485\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Projective image \(D_{3}\)
Projective field Galois closure of 3.1.83.1
Artin image size \(6\)
Artin image $S_3$
Artin field Galois closure of 3.1.83.1

$q$-expansion

\(f(q)\) \(=\) \( q - q^{3} + q^{4} - q^{7} + O(q^{10}) \) \( q - q^{3} + q^{4} - q^{7} - q^{11} - q^{12} + q^{16} - q^{17} + q^{21} + 2q^{23} + q^{25} + q^{27} - q^{28} - q^{29} - q^{31} + q^{33} - q^{37} + 2q^{41} - q^{44} - q^{48} + q^{51} - q^{59} - q^{61} + q^{64} - q^{68} - 2q^{69} - q^{75} + q^{77} - q^{81} + q^{83} + q^{84} + q^{87} + 2q^{92} + q^{93} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/83\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
82.1
0
0 −1.00000 1.00000 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
83.b Odd 1 CM by \(\Q(\sqrt{-83}) \) yes

Hecke kernels

There are no other newforms in \(S_{1}^{\mathrm{new}}(83, [\chi])\).