Properties

Label 280.3.c.d
Level $280$
Weight $3$
Character orbit 280.c
Self dual yes
Analytic conductor $7.629$
Analytic rank $0$
Dimension $1$
CM discriminant -280
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 280.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(7.62944740209\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{U}(1)[D_{2}]$

$q$-expansion

\(f(q)\) \(=\) \( q + 2q^{2} + 4q^{4} + 5q^{5} - 7q^{7} + 8q^{8} + 9q^{9} + O(q^{10}) \) \( q + 2q^{2} + 4q^{4} + 5q^{5} - 7q^{7} + 8q^{8} + 9q^{9} + 10q^{10} - 14q^{14} + 16q^{16} + 6q^{17} + 18q^{18} - 18q^{19} + 20q^{20} + 25q^{25} - 28q^{28} + 32q^{32} + 12q^{34} - 35q^{35} + 36q^{36} - 66q^{37} - 36q^{38} + 40q^{40} - 54q^{43} + 45q^{45} + 66q^{47} + 49q^{49} + 50q^{50} - 34q^{53} - 56q^{56} + 62q^{59} - 102q^{61} - 63q^{63} + 64q^{64} - 6q^{67} + 24q^{68} - 70q^{70} - 138q^{71} + 72q^{72} - 106q^{73} - 132q^{74} - 72q^{76} - 122q^{79} + 80q^{80} + 81q^{81} + 30q^{85} - 108q^{86} + 90q^{90} + 132q^{94} - 90q^{95} + 166q^{97} + 98q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).

\(n\) \(57\) \(71\) \(141\) \(241\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
69.1
0
2.00000 0 4.00000 5.00000 0 −7.00000 8.00000 9.00000 10.0000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
280.c odd 2 1 CM by \(\Q(\sqrt{-70}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 280.3.c.d yes 1
4.b odd 2 1 1120.3.c.d 1
5.b even 2 1 280.3.c.b yes 1
7.b odd 2 1 280.3.c.c yes 1
8.b even 2 1 280.3.c.a 1
8.d odd 2 1 1120.3.c.b 1
20.d odd 2 1 1120.3.c.c 1
28.d even 2 1 1120.3.c.a 1
35.c odd 2 1 280.3.c.a 1
40.e odd 2 1 1120.3.c.a 1
40.f even 2 1 280.3.c.c yes 1
56.e even 2 1 1120.3.c.c 1
56.h odd 2 1 280.3.c.b yes 1
140.c even 2 1 1120.3.c.b 1
280.c odd 2 1 CM 280.3.c.d yes 1
280.n even 2 1 1120.3.c.d 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
280.3.c.a 1 8.b even 2 1
280.3.c.a 1 35.c odd 2 1
280.3.c.b yes 1 5.b even 2 1
280.3.c.b yes 1 56.h odd 2 1
280.3.c.c yes 1 7.b odd 2 1
280.3.c.c yes 1 40.f even 2 1
280.3.c.d yes 1 1.a even 1 1 trivial
280.3.c.d yes 1 280.c odd 2 1 CM
1120.3.c.a 1 28.d even 2 1
1120.3.c.a 1 40.e odd 2 1
1120.3.c.b 1 8.d odd 2 1
1120.3.c.b 1 140.c even 2 1
1120.3.c.c 1 20.d odd 2 1
1120.3.c.c 1 56.e even 2 1
1120.3.c.d 1 4.b odd 2 1
1120.3.c.d 1 280.n even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{3}^{\mathrm{new}}(280, [\chi])\):

\( T_{3} \)
\( T_{17} - 6 \)
\( T_{19} + 18 \)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( -2 + T \)
$3$ \( T \)
$5$ \( -5 + T \)
$7$ \( 7 + T \)
$11$ \( T \)
$13$ \( T \)
$17$ \( -6 + T \)
$19$ \( 18 + T \)
$23$ \( T \)
$29$ \( T \)
$31$ \( T \)
$37$ \( 66 + T \)
$41$ \( T \)
$43$ \( 54 + T \)
$47$ \( -66 + T \)
$53$ \( 34 + T \)
$59$ \( -62 + T \)
$61$ \( 102 + T \)
$67$ \( 6 + T \)
$71$ \( 138 + T \)
$73$ \( 106 + T \)
$79$ \( 122 + T \)
$83$ \( T \)
$89$ \( T \)
$97$ \( -166 + T \)
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