Properties

 Label 547.1.b.a Level 547 Weight 1 Character orbit 547.b Self dual yes Analytic conductor 0.273 Analytic rank 0 Dimension 1 Projective image $$D_{3}$$ CM discriminant -547 Inner twists 2

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$547$$ Weight: $$k$$ $$=$$ $$1$$ Character orbit: $$[\chi]$$ $$=$$ 547.b (of order $$2$$, degree $$1$$, minimal)

Newform invariants

 Self dual: yes Analytic conductor: $$0.272988561910$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Projective image $$D_{3}$$ Projective field Galois closure of 3.1.547.1 Artin image $S_3$ Artin field Galois closure of 3.1.547.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q + q^{4} + q^{9} + O(q^{10})$$ $$q + q^{4} + q^{9} - q^{11} - q^{13} + q^{16} - q^{19} + q^{25} - q^{29} + q^{36} - q^{44} - q^{47} + q^{49} - q^{52} - q^{53} + q^{64} - q^{67} - q^{73} - q^{76} + q^{81} - q^{97} - q^{99} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/547\mathbb{Z}\right)^\times$$.

 $$n$$ $$2$$ $$\chi(n)$$ $$-1$$

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 $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
546.1
 0
0 0 1.00000 0 0 0 0 1.00000 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
547.b odd 2 1 CM by $$\Q(\sqrt{-547})$$

Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 547.1.b.a 1
547.b odd 2 1 CM 547.1.b.a 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
547.1.b.a 1 1.a even 1 1 trivial
547.1.b.a 1 547.b odd 2 1 CM

Hecke kernels

This newform subspace is the entire newspace $$S_{1}^{\mathrm{new}}(547, [\chi])$$.

Hecke characteristic polynomials

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