Properties

 Label 2563.1.b.a Level 2563 Weight 1 Character orbit 2563.b Self dual yes Analytic conductor 1.279 Analytic rank 0 Dimension 1 Projective image $$D_{3}$$ CM discriminant -2563 Inner twists 2

Related objects

Newspace parameters

 Level: $$N$$ = $$2563 = 11 \cdot 233$$ Weight: $$k$$ = $$1$$ Character orbit: $$[\chi]$$ = 2563.b (of order $$2$$, degree $$1$$, minimal)

Newform invariants

 Self dual: yes Analytic conductor: $$1.27910362738$$ 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 3.1.2563.1 Artin image $D_6$ Artin field Galois closure of 6.0.72258659.1

$q$-expansion

 $$f(q)$$ $$=$$ $$q + q^{4} + q^{9} + O(q^{10})$$ $$q + q^{4} + q^{9} - q^{11} + q^{16} + q^{17} - q^{23} + q^{25} - q^{31} + q^{36} - q^{37} + q^{41} + q^{43} - q^{44} + q^{49} - 2q^{61} + q^{64} + q^{68} - q^{71} + q^{73} + q^{79} + q^{81} - 2q^{83} - q^{89} - q^{92} - q^{99} + O(q^{100})$$

Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/2563\mathbb{Z}\right)^\times$$.

 $$n$$ $$1399$$ $$2333$$ $$\chi(n)$$ $$-1$$ $$-1$$

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 $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
2562.1
 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
2563.b odd 2 1 CM by $$\Q(\sqrt{-2563})$$

Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2563.1.b.a 1
11.b odd 2 1 2563.1.b.b yes 1
233.b even 2 1 2563.1.b.b yes 1
2563.b odd 2 1 CM 2563.1.b.a 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2563.1.b.a 1 1.a even 1 1 trivial
2563.1.b.a 1 2563.b odd 2 1 CM
2563.1.b.b yes 1 11.b odd 2 1
2563.1.b.b yes 1 233.b even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{1}^{\mathrm{new}}(2563, [\chi])$$:

 $$T_{2}$$ $$T_{17} - 1$$

Hecke Characteristic Polynomials

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