Properties

Label 1840.1.g.a
Level $1840$
Weight $1$
Character orbit 1840.g
Self dual yes
Analytic conductor $0.918$
Analytic rank $0$
Dimension $1$
Projective image $D_{3}$
CM discriminant -115
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1840.g (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: yes
Analytic conductor: \(0.918279623245\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 460)
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.460.1
Artin image: $D_6$
Artin field: Galois closure of 6.0.16928000.1

$q$-expansion

\(f(q)\) \(=\) \( q - q^{5} - q^{7} + q^{9} + O(q^{10}) \) \( q - q^{5} - q^{7} + q^{9} + q^{17} + q^{23} + q^{25} - q^{29} + q^{31} + q^{35} + q^{37} - q^{41} + 2q^{43} - q^{45} + q^{53} + q^{59} - q^{63} - q^{67} + q^{71} + q^{81} - q^{83} - q^{85} - 2q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1840\mathbb{Z}\right)^\times\).

\(n\) \(737\) \(1151\) \(1201\) \(1381\)
\(\chi(n)\) \(-1\) \(1\) \(-1\) \(1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
689.1
0
0 0 0 −1.00000 0 −1.00000 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
115.c odd 2 1 CM by \(\Q(\sqrt{-115}) \)

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1840.1.g.a 1
4.b odd 2 1 460.1.d.a 1
5.b even 2 1 1840.1.g.b 1
20.d odd 2 1 460.1.d.b yes 1
20.e even 4 2 2300.1.f.a 2
23.b odd 2 1 1840.1.g.b 1
92.b even 2 1 460.1.d.b yes 1
115.c odd 2 1 CM 1840.1.g.a 1
460.g even 2 1 460.1.d.a 1
460.k odd 4 2 2300.1.f.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
460.1.d.a 1 4.b odd 2 1
460.1.d.a 1 460.g even 2 1
460.1.d.b yes 1 20.d odd 2 1
460.1.d.b yes 1 92.b even 2 1
1840.1.g.a 1 1.a even 1 1 trivial
1840.1.g.a 1 115.c odd 2 1 CM
1840.1.g.b 1 5.b even 2 1
1840.1.g.b 1 23.b odd 2 1
2300.1.f.a 2 20.e even 4 2
2300.1.f.a 2 460.k odd 4 2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{7} + 1 \) acting on \(S_{1}^{\mathrm{new}}(1840, [\chi])\).

Hecke characteristic polynomials

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