Properties

Label 819.1.d.a
Level $819$
Weight $1$
Character orbit 819.d
Self dual yes
Analytic conductor $0.409$
Analytic rank $0$
Dimension $1$
Projective image $D_{2}$
CM/RM discs -3, -91, 273
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 819.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.408734245346\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{2}\)
Projective field: Galois closure of \(\Q(\sqrt{-3}, \sqrt{-91})\)
Artin image: $D_4$
Artin field: Galois closure of 4.0.2457.2

$q$-expansion

\(f(q)\) \(=\) \( q + q^{4} - q^{7} + O(q^{10}) \) \( q + q^{4} - q^{7} + q^{13} + q^{16} + 2q^{19} - q^{25} - q^{28} - 2q^{31} - 2q^{43} + q^{49} + q^{52} + q^{64} - 2q^{73} + 2q^{76} - 2q^{79} - q^{91} + 2q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
181.1
0
0 0 1.00000 0 0 −1.00000 0 0 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 CM by \(\Q(\sqrt{-3}) \)
91.b odd 2 1 CM by \(\Q(\sqrt{-91}) \)
273.g even 2 1 RM by \(\Q(\sqrt{273}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 819.1.d.a 1
3.b odd 2 1 CM 819.1.d.a 1
7.b odd 2 1 819.1.d.b yes 1
13.b even 2 1 819.1.d.b yes 1
21.c even 2 1 819.1.d.b yes 1
39.d odd 2 1 819.1.d.b yes 1
91.b odd 2 1 CM 819.1.d.a 1
273.g even 2 1 RM 819.1.d.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
819.1.d.a 1 1.a even 1 1 trivial
819.1.d.a 1 3.b odd 2 1 CM
819.1.d.a 1 91.b odd 2 1 CM
819.1.d.a 1 273.g even 2 1 RM
819.1.d.b yes 1 7.b odd 2 1
819.1.d.b yes 1 13.b even 2 1
819.1.d.b yes 1 21.c even 2 1
819.1.d.b yes 1 39.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{19} - 2 \) acting on \(S_{1}^{\mathrm{new}}(819, [\chi])\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \)
$3$ \( T \)
$5$ \( T \)
$7$ \( 1 + T \)
$11$ \( T \)
$13$ \( -1 + T \)
$17$ \( T \)
$19$ \( -2 + T \)
$23$ \( T \)
$29$ \( T \)
$31$ \( 2 + T \)
$37$ \( T \)
$41$ \( T \)
$43$ \( 2 + T \)
$47$ \( T \)
$53$ \( T \)
$59$ \( T \)
$61$ \( T \)
$67$ \( T \)
$71$ \( T \)
$73$ \( 2 + T \)
$79$ \( 2 + T \)
$83$ \( T \)
$89$ \( T \)
$97$ \( -2 + T \)
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