# 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 $2$

# Related objects

## 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

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

## 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: Complex embeddings Normalized embeddings Satake parameters Satake angles

## 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 $$S_{1}^{\mathrm{new}}(891, [\chi])$$.

## Hecke characteristic polynomials

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