Properties

Label 2563.1.b.b
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

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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 $S_3$
Artin field Galois closure of 3.1.2563.1

$q$-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:

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

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

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