Properties

Label 799.1.c.a
Level $799$
Weight $1$
Character orbit 799.c
Self dual yes
Analytic conductor $0.399$
Analytic rank $0$
Dimension $1$
Projective image $D_{2}$
CM/RM discs -47, -799, 17
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 799 = 17 \cdot 47 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 799.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.398752945094\)
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 \(\Q(\sqrt{17}, \sqrt{-47})\)
Artin image: $D_4$
Artin field: Galois closure of 4.2.13583.1

$q$-expansion

\(f(q)\) \(=\) \( q - 2q^{2} + 3q^{4} - 4q^{8} + q^{9} + O(q^{10}) \) \( q - 2q^{2} + 3q^{4} - 4q^{8} + q^{9} + 5q^{16} + q^{17} - 2q^{18} - q^{25} - 6q^{32} - 2q^{34} + 3q^{36} + q^{47} + q^{49} + 2q^{50} + 2q^{53} - 2q^{59} + 7q^{64} + 3q^{68} - 4q^{72} + q^{81} + 2q^{83} + 2q^{89} - 2q^{94} - 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/799\mathbb{Z}\right)^\times\).

\(n\) \(52\) \(377\)
\(\chi(n)\) \(-1\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
798.1
0
−2.00000 0 3.00000 0 0 0 −4.00000 1.00000 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
17.b even 2 1 RM by \(\Q(\sqrt{17}) \)
47.b odd 2 1 CM by \(\Q(\sqrt{-47}) \)
799.c odd 2 1 CM by \(\Q(\sqrt{-799}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 799.1.c.a 1
17.b even 2 1 RM 799.1.c.a 1
47.b odd 2 1 CM 799.1.c.a 1
799.c odd 2 1 CM 799.1.c.a 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
799.1.c.a 1 1.a even 1 1 trivial
799.1.c.a 1 17.b even 2 1 RM
799.1.c.a 1 47.b odd 2 1 CM
799.1.c.a 1 799.c odd 2 1 CM

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} + 2 \) acting on \(S_{1}^{\mathrm{new}}(799, [\chi])\).

Hecke characteristic polynomials

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