Properties

Label 891.1.c.b
Level $891$
Weight $1$
Character orbit 891.c
Self dual yes
Analytic conductor $0.445$
Analytic rank $0$
Dimension $1$
Projective image $D_{3}$
CM discriminant -11
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 891.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.444666926256\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 99)
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.891.1
Artin image: $D_6$
Artin field: Galois closure of 6.0.2381643.1

$q$-expansion

\(f(q)\) \(=\) \( q + q^{4} + q^{5}+O(q^{10}) \) Copy content Toggle raw display \( q + q^{4} + q^{5} - q^{11} + q^{16} + q^{20} - 2 q^{23} - q^{31} - q^{37} - q^{44} + q^{47} + q^{49} + q^{53} - q^{55} + q^{59} + q^{64} - q^{67} + q^{71} + q^{80} - 2 q^{89} - 2 q^{92} - q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/891\mathbb{Z}\right)^\times\).

\(n\) \(244\) \(650\)
\(\chi(n)\) \(-1\) \(1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
406.1
0
0 0 1.00000 1.00000 0 0 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
11.b odd 2 1 CM by \(\Q(\sqrt{-11}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 891.1.c.b 1
3.b odd 2 1 891.1.c.a 1
9.c even 3 2 297.1.h.a 2
9.d odd 6 2 99.1.h.a 2
11.b odd 2 1 CM 891.1.c.b 1
33.d even 2 1 891.1.c.a 1
36.h even 6 2 1584.1.bf.b 2
45.h odd 6 2 2475.1.y.a 2
45.l even 12 4 2475.1.t.a 4
99.g even 6 2 99.1.h.a 2
99.h odd 6 2 297.1.h.a 2
99.m even 15 8 3267.1.w.a 8
99.n odd 30 8 1089.1.s.a 8
99.o odd 30 8 3267.1.w.a 8
99.p even 30 8 1089.1.s.a 8
396.o odd 6 2 1584.1.bf.b 2
495.r even 6 2 2475.1.y.a 2
495.bd odd 12 4 2475.1.t.a 4
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
99.1.h.a 2 9.d odd 6 2
99.1.h.a 2 99.g even 6 2
297.1.h.a 2 9.c even 3 2
297.1.h.a 2 99.h odd 6 2
891.1.c.a 1 3.b odd 2 1
891.1.c.a 1 33.d even 2 1
891.1.c.b 1 1.a even 1 1 trivial
891.1.c.b 1 11.b odd 2 1 CM
1089.1.s.a 8 99.n odd 30 8
1089.1.s.a 8 99.p even 30 8
1584.1.bf.b 2 36.h even 6 2
1584.1.bf.b 2 396.o odd 6 2
2475.1.t.a 4 45.l even 12 4
2475.1.t.a 4 495.bd odd 12 4
2475.1.y.a 2 45.h odd 6 2
2475.1.y.a 2 495.r even 6 2
3267.1.w.a 8 99.m even 15 8
3267.1.w.a 8 99.o odd 30 8

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5} - 1 \) acting on \(S_{1}^{\mathrm{new}}(891, [\chi])\). 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
$23$ \( T + 2 \) Copy content Toggle raw display
$29$ \( T \) Copy content Toggle raw display
$31$ \( T + 1 \) Copy content Toggle raw display
$37$ \( T + 1 \) Copy content Toggle raw display
$41$ \( T \) Copy content Toggle raw display
$43$ \( T \) Copy content Toggle raw display
$47$ \( T - 1 \) Copy content Toggle raw display
$53$ \( T - 1 \) Copy content Toggle raw display
$59$ \( T - 1 \) Copy content Toggle raw display
$61$ \( T \) Copy content Toggle raw display
$67$ \( T + 1 \) Copy content Toggle raw display
$71$ \( T - 1 \) 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
$97$ \( T + 1 \) Copy content Toggle raw display
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