Properties

Label 2880.1.bh.a
Level $2880$
Weight $1$
Character orbit 2880.bh
Analytic conductor $1.437$
Analytic rank $0$
Dimension $2$
Projective image $D_{4}$
CM discriminant -4
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2880.bh (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.43730723638\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1440)
Projective image: \(D_{4}\)
Projective field: Galois closure of 4.2.18000.1

$q$-expansion

The \(q\)-expansion and trace form are shown below.

\(f(q)\) \(=\) \( q - q^{5}+O(q^{10}) \) Copy content Toggle raw display \( q - q^{5} + ( - i - 1) q^{13} + (i - 1) q^{17} + q^{25} + i q^{29} + (i - 1) q^{37} - q^{41} + i q^{49} + ( - i - 1) q^{53} + (i + 1) q^{65} + ( - i - 1) q^{73} + ( - i + 1) q^{85} - i q^{89} + (i - 1) q^{97} +O(q^{100}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{5} - 2 q^{13} - 2 q^{17} + 2 q^{25} - 2 q^{37} - 4 q^{41} - 2 q^{53} + 2 q^{65} - 2 q^{73} + 2 q^{85} - 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(641\) \(901\) \(2431\)
\(\chi(n)\) \(-i\) \(1\) \(1\) \(1\)

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
577.1
1.00000i
1.00000i
0 0 0 −1.00000 0 0 0 0 0
1153.1 0 0 0 −1.00000 0 0 0 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
4.b odd 2 1 CM by \(\Q(\sqrt{-1}) \)
5.c odd 4 1 inner
20.e even 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2880.1.bh.a 2
3.b odd 2 1 2880.1.bh.c 2
4.b odd 2 1 CM 2880.1.bh.a 2
5.c odd 4 1 inner 2880.1.bh.a 2
8.b even 2 1 1440.1.bh.c yes 2
8.d odd 2 1 1440.1.bh.c yes 2
12.b even 2 1 2880.1.bh.c 2
15.e even 4 1 2880.1.bh.c 2
20.e even 4 1 inner 2880.1.bh.a 2
24.f even 2 1 1440.1.bh.a 2
24.h odd 2 1 1440.1.bh.a 2
40.i odd 4 1 1440.1.bh.c yes 2
40.k even 4 1 1440.1.bh.c yes 2
60.l odd 4 1 2880.1.bh.c 2
120.q odd 4 1 1440.1.bh.a 2
120.w even 4 1 1440.1.bh.a 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1440.1.bh.a 2 24.f even 2 1
1440.1.bh.a 2 24.h odd 2 1
1440.1.bh.a 2 120.q odd 4 1
1440.1.bh.a 2 120.w even 4 1
1440.1.bh.c yes 2 8.b even 2 1
1440.1.bh.c yes 2 8.d odd 2 1
1440.1.bh.c yes 2 40.i odd 4 1
1440.1.bh.c yes 2 40.k even 4 1
2880.1.bh.a 2 1.a even 1 1 trivial
2880.1.bh.a 2 4.b odd 2 1 CM
2880.1.bh.a 2 5.c odd 4 1 inner
2880.1.bh.a 2 20.e even 4 1 inner
2880.1.bh.c 2 3.b odd 2 1
2880.1.bh.c 2 12.b even 2 1
2880.1.bh.c 2 15.e even 4 1
2880.1.bh.c 2 60.l odd 4 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(2880, [\chi])\):

\( T_{13}^{2} + 2T_{13} + 2 \) Copy content Toggle raw display
\( T_{17}^{2} + 2T_{17} + 2 \) Copy content Toggle raw display

Hecke characteristic polynomials

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