Properties

Label 1088.1.g.a
Level $1088$
Weight $1$
Character orbit 1088.g
Self dual yes
Analytic conductor $0.543$
Analytic rank $0$
Dimension $1$
Projective image $D_{2}$
CM/RM discs -4, -68, 17
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1088 = 2^{6} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1088.g (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.542982733745\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 68)
Projective image: \(D_{2}\)
Projective field: Galois closure of \(\Q(i, \sqrt{17})\)
Artin image: $D_4$
Artin field: Galois closure of 4.0.4352.2

$q$-expansion

\(f(q)\) \(=\) \( q - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{9} + 2 q^{13} + q^{17} + q^{25} - q^{49} - 2 q^{53} + q^{81} - 2 q^{89}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1088\mathbb{Z}\right)^\times\).

\(n\) \(69\) \(511\) \(513\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1087.1
0
0 0 0 0 0 0 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
4.b odd 2 1 CM by \(\Q(\sqrt{-1}) \)
17.b even 2 1 RM by \(\Q(\sqrt{17}) \)
68.d odd 2 1 CM by \(\Q(\sqrt{-17}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1088.1.g.a 1
4.b odd 2 1 CM 1088.1.g.a 1
8.b even 2 1 68.1.d.a 1
8.d odd 2 1 68.1.d.a 1
17.b even 2 1 RM 1088.1.g.a 1
24.f even 2 1 612.1.e.a 1
24.h odd 2 1 612.1.e.a 1
40.e odd 2 1 1700.1.h.d 1
40.f even 2 1 1700.1.h.d 1
40.i odd 4 2 1700.1.d.b 2
40.k even 4 2 1700.1.d.b 2
56.e even 2 1 3332.1.g.a 1
56.h odd 2 1 3332.1.g.a 1
56.j odd 6 2 3332.1.o.d 2
56.k odd 6 2 3332.1.o.c 2
56.m even 6 2 3332.1.o.d 2
56.p even 6 2 3332.1.o.c 2
68.d odd 2 1 CM 1088.1.g.a 1
136.e odd 2 1 68.1.d.a 1
136.h even 2 1 68.1.d.a 1
136.i even 4 2 1156.1.c.a 1
136.j odd 4 2 1156.1.c.a 1
136.o even 8 4 1156.1.f.a 2
136.p odd 8 4 1156.1.f.a 2
136.q odd 16 8 1156.1.g.a 4
136.s even 16 8 1156.1.g.a 4
408.b odd 2 1 612.1.e.a 1
408.h even 2 1 612.1.e.a 1
680.h even 2 1 1700.1.h.d 1
680.k odd 2 1 1700.1.h.d 1
680.u even 4 2 1700.1.d.b 2
680.bi odd 4 2 1700.1.d.b 2
952.e odd 2 1 3332.1.g.a 1
952.k even 2 1 3332.1.g.a 1
952.z even 6 2 3332.1.o.c 2
952.bf even 6 2 3332.1.o.d 2
952.bi odd 6 2 3332.1.o.c 2
952.bl odd 6 2 3332.1.o.d 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
68.1.d.a 1 8.b even 2 1
68.1.d.a 1 8.d odd 2 1
68.1.d.a 1 136.e odd 2 1
68.1.d.a 1 136.h even 2 1
612.1.e.a 1 24.f even 2 1
612.1.e.a 1 24.h odd 2 1
612.1.e.a 1 408.b odd 2 1
612.1.e.a 1 408.h even 2 1
1088.1.g.a 1 1.a even 1 1 trivial
1088.1.g.a 1 4.b odd 2 1 CM
1088.1.g.a 1 17.b even 2 1 RM
1088.1.g.a 1 68.d odd 2 1 CM
1156.1.c.a 1 136.i even 4 2
1156.1.c.a 1 136.j odd 4 2
1156.1.f.a 2 136.o even 8 4
1156.1.f.a 2 136.p odd 8 4
1156.1.g.a 4 136.q odd 16 8
1156.1.g.a 4 136.s even 16 8
1700.1.d.b 2 40.i odd 4 2
1700.1.d.b 2 40.k even 4 2
1700.1.d.b 2 680.u even 4 2
1700.1.d.b 2 680.bi odd 4 2
1700.1.h.d 1 40.e odd 2 1
1700.1.h.d 1 40.f even 2 1
1700.1.h.d 1 680.h even 2 1
1700.1.h.d 1 680.k odd 2 1
3332.1.g.a 1 56.e even 2 1
3332.1.g.a 1 56.h odd 2 1
3332.1.g.a 1 952.e odd 2 1
3332.1.g.a 1 952.k even 2 1
3332.1.o.c 2 56.k odd 6 2
3332.1.o.c 2 56.p even 6 2
3332.1.o.c 2 952.z even 6 2
3332.1.o.c 2 952.bi odd 6 2
3332.1.o.d 2 56.j odd 6 2
3332.1.o.d 2 56.m even 6 2
3332.1.o.d 2 952.bf even 6 2
3332.1.o.d 2 952.bl odd 6 2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} \) acting on \(S_{1}^{\mathrm{new}}(1088, [\chi])\). Copy content Toggle raw display

Hecke characteristic polynomials

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