Properties

Label 2520.1.h.a
Level $2520$
Weight $1$
Character orbit 2520.h
Self dual yes
Analytic conductor $1.258$
Analytic rank $0$
Dimension $1$
Projective image $D_{2}$
CM/RM discs -24, -280, 105
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2520.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(1.25764383184\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{2}\)
Projective field: Galois closure of \(\Q(\sqrt{-6}, \sqrt{-70})\)
Artin image: $D_4$
Artin field: Galois closure of 4.0.60480.2

$q$-expansion

\(f(q)\) \(=\) \( q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + O(q^{10}) \) \( q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} + q^{14} + q^{16} - q^{20} + q^{25} - q^{28} - q^{32} + q^{35} + q^{40} + q^{49} - q^{50} + 2q^{53} + q^{56} + 2q^{59} + q^{64} - q^{70} + 2q^{73} - 2q^{79} - q^{80} - 2q^{97} - q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).

\(n\) \(281\) \(631\) \(1081\) \(1261\) \(2017\)
\(\chi(n)\) \(1\) \(1\) \(-1\) \(-1\) \(-1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1189.1
0
−1.00000 0 1.00000 −1.00000 0 −1.00000 −1.00000 0 1.00000
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
24.h odd 2 1 CM by \(\Q(\sqrt{-6}) \)
105.g even 2 1 RM by \(\Q(\sqrt{105}) \)
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 2520.1.h.a 1
3.b odd 2 1 2520.1.h.d yes 1
5.b even 2 1 2520.1.h.c yes 1
7.b odd 2 1 2520.1.h.b yes 1
8.b even 2 1 2520.1.h.d yes 1
15.d odd 2 1 2520.1.h.b yes 1
21.c even 2 1 2520.1.h.c yes 1
24.h odd 2 1 CM 2520.1.h.a 1
35.c odd 2 1 2520.1.h.d yes 1
40.f even 2 1 2520.1.h.b yes 1
56.h odd 2 1 2520.1.h.c yes 1
105.g even 2 1 RM 2520.1.h.a 1
120.i odd 2 1 2520.1.h.c yes 1
168.i even 2 1 2520.1.h.b yes 1
280.c odd 2 1 CM 2520.1.h.a 1
840.u even 2 1 2520.1.h.d yes 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2520.1.h.a 1 1.a even 1 1 trivial
2520.1.h.a 1 24.h odd 2 1 CM
2520.1.h.a 1 105.g even 2 1 RM
2520.1.h.a 1 280.c odd 2 1 CM
2520.1.h.b yes 1 7.b odd 2 1
2520.1.h.b yes 1 15.d odd 2 1
2520.1.h.b yes 1 40.f even 2 1
2520.1.h.b yes 1 168.i even 2 1
2520.1.h.c yes 1 5.b even 2 1
2520.1.h.c yes 1 21.c even 2 1
2520.1.h.c yes 1 56.h odd 2 1
2520.1.h.c yes 1 120.i odd 2 1
2520.1.h.d yes 1 3.b odd 2 1
2520.1.h.d yes 1 8.b even 2 1
2520.1.h.d yes 1 35.c odd 2 1
2520.1.h.d yes 1 840.u even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(2520, [\chi])\):

\( T_{13} \)
\( T_{53} - 2 \)
\( T_{59} - 2 \)

Hecke characteristic polynomials

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