Properties

Label 2583.1.f.b
Level 2583
Weight 1
Character orbit 2583.f
Self dual yes
Analytic conductor 1.289
Analytic rank 0
Dimension 3
Projective image \(D_{7}\)
CM discriminant -287
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 2583 = 3^{2} \cdot 7 \cdot 41 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2583.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(1.28908492763\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: \(\Q(\zeta_{14})^+\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 287)
Projective image \(D_{7}\)
Projective field Galois closure of 7.1.23639903.1
Artin image $D_{14}$
Artin field Galois closure of \(\mathbb{Q}[x]/(x^{14} + \cdots)\)

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a root \(\beta\) of the polynomial \(x^{3} - x^{2} - 2 x + 1\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\) \(=\) \( q + \beta q^{2} + ( -1 + \beta^{2} ) q^{4} + q^{7} + ( -1 + \beta^{2} ) q^{8} +O(q^{10})\) \( q + \beta q^{2} + ( -1 + \beta^{2} ) q^{4} + q^{7} + ( -1 + \beta^{2} ) q^{8} -\beta q^{13} + \beta q^{14} + \beta q^{16} + ( -1 - \beta + \beta^{2} ) q^{17} + ( 1 + \beta - \beta^{2} ) q^{19} + ( 2 - \beta^{2} ) q^{23} + q^{25} -\beta^{2} q^{26} + ( -1 + \beta^{2} ) q^{28} + q^{32} + ( -1 + \beta ) q^{34} -\beta q^{37} + ( 1 - \beta ) q^{38} - q^{41} + ( 1 + \beta - \beta^{2} ) q^{43} + ( 1 - \beta^{2} ) q^{46} + \beta q^{47} + q^{49} + \beta q^{50} + ( 1 - \beta - \beta^{2} ) q^{52} + ( -1 + \beta^{2} ) q^{56} + q^{68} -\beta^{2} q^{74} - q^{76} -\beta q^{82} + ( 1 - \beta ) q^{86} + \beta q^{89} -\beta q^{91} + ( -1 - \beta ) q^{92} + \beta^{2} q^{94} + ( -2 + \beta^{2} ) q^{97} + \beta q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q + q^{2} + 2q^{4} + 3q^{7} + 2q^{8} + O(q^{10}) \) \( 3q + q^{2} + 2q^{4} + 3q^{7} + 2q^{8} - q^{13} + q^{14} + q^{16} + q^{17} - q^{19} + q^{23} + 3q^{25} - 5q^{26} + 2q^{28} + 3q^{32} - 2q^{34} - q^{37} + 2q^{38} - 3q^{41} - q^{43} - 2q^{46} + q^{47} + 3q^{49} + q^{50} - 3q^{52} + 2q^{56} + 3q^{68} - 5q^{74} - 3q^{76} - q^{82} + 2q^{86} + q^{89} - q^{91} - 4q^{92} + 5q^{94} - q^{97} + q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2583\mathbb{Z}\right)^\times\).

\(n\) \(1072\) \(2215\) \(2297\)
\(\chi(n)\) \(-1\) \(-1\) \(1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2008.1
−1.24698
0.445042
1.80194
−1.24698 0 0.554958 0 0 1.00000 0.554958 0 0
2008.2 0.445042 0 −0.801938 0 0 1.00000 −0.801938 0 0
2008.3 1.80194 0 2.24698 0 0 1.00000 2.24698 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
287.d odd 2 1 CM by \(\Q(\sqrt{-287}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2583.1.f.b 3
3.b odd 2 1 287.1.d.a 3
7.b odd 2 1 2583.1.f.a 3
21.c even 2 1 287.1.d.b yes 3
21.g even 6 2 2009.1.i.a 6
21.h odd 6 2 2009.1.i.b 6
41.b even 2 1 2583.1.f.a 3
123.b odd 2 1 287.1.d.b yes 3
287.d odd 2 1 CM 2583.1.f.b 3
861.e even 2 1 287.1.d.a 3
861.r even 6 2 2009.1.i.b 6
861.t odd 6 2 2009.1.i.a 6
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
287.1.d.a 3 3.b odd 2 1
287.1.d.a 3 861.e even 2 1
287.1.d.b yes 3 21.c even 2 1
287.1.d.b yes 3 123.b odd 2 1
2009.1.i.a 6 21.g even 6 2
2009.1.i.a 6 861.t odd 6 2
2009.1.i.b 6 21.h odd 6 2
2009.1.i.b 6 861.r even 6 2
2583.1.f.a 3 7.b odd 2 1
2583.1.f.a 3 41.b even 2 1
2583.1.f.b 3 1.a even 1 1 trivial
2583.1.f.b 3 287.d odd 2 1 CM

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{13}^{3} + T_{13}^{2} - 2 T_{13} - 1 \) acting on \(S_{1}^{\mathrm{new}}(2583, [\chi])\).

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} \)
$3$ 1
$5$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$7$ \( ( 1 - T )^{3} \)
$11$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$13$ \( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \)
$17$ \( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} \)
$19$ \( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \)
$23$ \( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} \)
$29$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$31$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$37$ \( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \)
$41$ \( ( 1 + T )^{3} \)
$43$ \( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \)
$47$ \( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} \)
$53$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$59$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$61$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$67$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$71$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$73$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$79$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$83$ \( ( 1 - T )^{3}( 1 + T )^{3} \)
$89$ \( 1 - T + T^{2} - T^{3} + T^{4} - T^{5} + T^{6} \)
$97$ \( 1 + T + T^{2} + T^{3} + T^{4} + T^{5} + T^{6} \)
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