Properties

Label 1792.1.c.b
Level $1792$
Weight $1$
Character orbit 1792.c
Self dual yes
Analytic conductor $0.894$
Analytic rank $0$
Dimension $1$
Projective image $D_{2}$
CM/RM discs -7, -56, 8
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1792.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.894324502638\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 56)
Projective image: \(D_{2}\)
Projective field: Galois closure of \(\Q(\sqrt{2}, \sqrt{-7})\)
Artin image: $D_4$
Artin field: Galois closure of 4.2.14336.1

$q$-expansion

\(f(q)\) \(=\) \( q + q^{7} + q^{9} + O(q^{10}) \) \( q + q^{7} + q^{9} - 2q^{23} + q^{25} + q^{49} + q^{63} + 2q^{71} - 2q^{79} + q^{81} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).

\(n\) \(1023\) \(1025\) \(1541\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
769.1
0
0 0 0 0 0 1.00000 0 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
7.b odd 2 1 CM by \(\Q(\sqrt{-7}) \)
8.b even 2 1 RM by \(\Q(\sqrt{2}) \)
56.h odd 2 1 CM by \(\Q(\sqrt{-14}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1792.1.c.b 1
4.b odd 2 1 1792.1.c.a 1
7.b odd 2 1 CM 1792.1.c.b 1
8.b even 2 1 RM 1792.1.c.b 1
8.d odd 2 1 1792.1.c.a 1
16.e even 4 2 56.1.h.a 1
16.f odd 4 2 224.1.h.a 1
28.d even 2 1 1792.1.c.a 1
48.i odd 4 2 504.1.l.a 1
48.k even 4 2 2016.1.l.a 1
56.e even 2 1 1792.1.c.a 1
56.h odd 2 1 CM 1792.1.c.b 1
80.i odd 4 2 1400.1.c.a 2
80.q even 4 2 1400.1.m.a 1
80.t odd 4 2 1400.1.c.a 2
112.j even 4 2 224.1.h.a 1
112.l odd 4 2 56.1.h.a 1
112.u odd 12 4 1568.1.n.a 2
112.v even 12 4 1568.1.n.a 2
112.w even 12 4 392.1.j.a 2
112.x odd 12 4 392.1.j.a 2
336.v odd 4 2 2016.1.l.a 1
336.y even 4 2 504.1.l.a 1
336.bo even 12 4 3528.1.bw.a 2
336.bt odd 12 4 3528.1.bw.a 2
560.r even 4 2 1400.1.c.a 2
560.bf odd 4 2 1400.1.m.a 1
560.bn even 4 2 1400.1.c.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
56.1.h.a 1 16.e even 4 2
56.1.h.a 1 112.l odd 4 2
224.1.h.a 1 16.f odd 4 2
224.1.h.a 1 112.j even 4 2
392.1.j.a 2 112.w even 12 4
392.1.j.a 2 112.x odd 12 4
504.1.l.a 1 48.i odd 4 2
504.1.l.a 1 336.y even 4 2
1400.1.c.a 2 80.i odd 4 2
1400.1.c.a 2 80.t odd 4 2
1400.1.c.a 2 560.r even 4 2
1400.1.c.a 2 560.bn even 4 2
1400.1.m.a 1 80.q even 4 2
1400.1.m.a 1 560.bf odd 4 2
1568.1.n.a 2 112.u odd 12 4
1568.1.n.a 2 112.v even 12 4
1792.1.c.a 1 4.b odd 2 1
1792.1.c.a 1 8.d odd 2 1
1792.1.c.a 1 28.d even 2 1
1792.1.c.a 1 56.e even 2 1
1792.1.c.b 1 1.a even 1 1 trivial
1792.1.c.b 1 7.b odd 2 1 CM
1792.1.c.b 1 8.b even 2 1 RM
1792.1.c.b 1 56.h odd 2 1 CM
2016.1.l.a 1 48.k even 4 2
2016.1.l.a 1 336.v odd 4 2
3528.1.bw.a 2 336.bo even 12 4
3528.1.bw.a 2 336.bt odd 12 4

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(1792, [\chi])\):

\( T_{3} \)
\( T_{23} + 2 \)
\( T_{71} - 2 \)

Hecke characteristic polynomials

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