Properties

Label 880.1.i.a
Level $880$
Weight $1$
Character orbit 880.i
Self dual yes
Analytic conductor $0.439$
Analytic rank $0$
Dimension $1$
Projective image $D_{2}$
CM/RM discs -11, -55, 5
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 880.i (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.439177211117\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 55)
Projective image: \(D_{2}\)
Projective field: Galois closure of \(\Q(\sqrt{5}, \sqrt{-11})\)
Artin image: $D_4$
Artin field: Galois closure of 4.2.4400.1

$q$-expansion

\(f(q)\) \(=\) \( q - q^{5} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{5} + q^{9} + q^{11} + q^{25} + 2 q^{31} - q^{45} - q^{49} - q^{55} - 2 q^{59} - 2 q^{71} + q^{81} - 2 q^{89} + q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/880\mathbb{Z}\right)^\times\).

\(n\) \(111\) \(177\) \(321\) \(661\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(1\)

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 −1.00000 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
5.b even 2 1 RM by \(\Q(\sqrt{5}) \)
11.b odd 2 1 CM by \(\Q(\sqrt{-11}) \)
55.d odd 2 1 CM by \(\Q(\sqrt{-55}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 880.1.i.a 1
4.b odd 2 1 55.1.d.a 1
5.b even 2 1 RM 880.1.i.a 1
8.b even 2 1 3520.1.i.a 1
8.d odd 2 1 3520.1.i.b 1
11.b odd 2 1 CM 880.1.i.a 1
12.b even 2 1 495.1.h.a 1
20.d odd 2 1 55.1.d.a 1
20.e even 4 2 275.1.c.a 1
28.d even 2 1 2695.1.g.c 1
28.f even 6 2 2695.1.q.b 2
28.g odd 6 2 2695.1.q.c 2
40.e odd 2 1 3520.1.i.b 1
40.f even 2 1 3520.1.i.a 1
44.c even 2 1 55.1.d.a 1
44.g even 10 4 605.1.h.a 4
44.h odd 10 4 605.1.h.a 4
55.d odd 2 1 CM 880.1.i.a 1
60.h even 2 1 495.1.h.a 1
60.l odd 4 2 2475.1.b.a 1
88.b odd 2 1 3520.1.i.a 1
88.g even 2 1 3520.1.i.b 1
132.d odd 2 1 495.1.h.a 1
140.c even 2 1 2695.1.g.c 1
140.p odd 6 2 2695.1.q.c 2
140.s even 6 2 2695.1.q.b 2
220.g even 2 1 55.1.d.a 1
220.i odd 4 2 275.1.c.a 1
220.n odd 10 4 605.1.h.a 4
220.o even 10 4 605.1.h.a 4
220.v even 20 8 3025.1.x.a 4
220.w odd 20 8 3025.1.x.a 4
308.g odd 2 1 2695.1.g.c 1
308.m odd 6 2 2695.1.q.b 2
308.n even 6 2 2695.1.q.c 2
440.c even 2 1 3520.1.i.b 1
440.o odd 2 1 3520.1.i.a 1
660.g odd 2 1 495.1.h.a 1
660.q even 4 2 2475.1.b.a 1
1540.b odd 2 1 2695.1.g.c 1
1540.be even 6 2 2695.1.q.c 2
1540.bj odd 6 2 2695.1.q.b 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
55.1.d.a 1 4.b odd 2 1
55.1.d.a 1 20.d odd 2 1
55.1.d.a 1 44.c even 2 1
55.1.d.a 1 220.g even 2 1
275.1.c.a 1 20.e even 4 2
275.1.c.a 1 220.i odd 4 2
495.1.h.a 1 12.b even 2 1
495.1.h.a 1 60.h even 2 1
495.1.h.a 1 132.d odd 2 1
495.1.h.a 1 660.g odd 2 1
605.1.h.a 4 44.g even 10 4
605.1.h.a 4 44.h odd 10 4
605.1.h.a 4 220.n odd 10 4
605.1.h.a 4 220.o even 10 4
880.1.i.a 1 1.a even 1 1 trivial
880.1.i.a 1 5.b even 2 1 RM
880.1.i.a 1 11.b odd 2 1 CM
880.1.i.a 1 55.d odd 2 1 CM
2475.1.b.a 1 60.l odd 4 2
2475.1.b.a 1 660.q even 4 2
2695.1.g.c 1 28.d even 2 1
2695.1.g.c 1 140.c even 2 1
2695.1.g.c 1 308.g odd 2 1
2695.1.g.c 1 1540.b odd 2 1
2695.1.q.b 2 28.f even 6 2
2695.1.q.b 2 140.s even 6 2
2695.1.q.b 2 308.m odd 6 2
2695.1.q.b 2 1540.bj odd 6 2
2695.1.q.c 2 28.g odd 6 2
2695.1.q.c 2 140.p odd 6 2
2695.1.q.c 2 308.n even 6 2
2695.1.q.c 2 1540.be even 6 2
3025.1.x.a 4 220.v even 20 8
3025.1.x.a 4 220.w odd 20 8
3520.1.i.a 1 8.b even 2 1
3520.1.i.a 1 40.f even 2 1
3520.1.i.a 1 88.b odd 2 1
3520.1.i.a 1 440.o odd 2 1
3520.1.i.b 1 8.d odd 2 1
3520.1.i.b 1 40.e odd 2 1
3520.1.i.b 1 88.g even 2 1
3520.1.i.b 1 440.c even 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} \) acting on \(S_{1}^{\mathrm{new}}(880, [\chi])\). 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
$5$ \( T + 1 \) Copy content Toggle raw display
$7$ \( T \) Copy content Toggle raw display
$11$ \( T - 1 \) Copy content Toggle raw display
$13$ \( T \) Copy content Toggle raw display
$17$ \( T \) 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
$31$ \( T - 2 \) 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
$53$ \( T \) Copy content Toggle raw display
$59$ \( T + 2 \) Copy content Toggle raw display
$61$ \( T \) Copy content Toggle raw display
$67$ \( T \) Copy content Toggle raw display
$71$ \( T + 2 \) 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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