Properties

Label 2880.1.j.b
Level 2880
Weight 1
Character orbit 2880.j
Analytic conductor 1.437
Analytic rank 0
Dimension 2
Projective image \(D_{2}\)
CM/RM discs -4, -15, 60
Inner twists 8

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(1.43730723638\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 180)
Projective image \(D_{2}\)
Projective field Galois closure of \(\Q(i, \sqrt{15})\)
Artin image $D_4:C_2$
Artin field Galois closure of 8.0.1194393600.9

$q$-expansion

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

\(f(q)\) \(=\) \( q -i q^{5} +O(q^{10})\) \( q -i q^{5} -2 i q^{17} - q^{25} - q^{49} -2 i q^{53} + 2 q^{61} -2 q^{85} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + O(q^{10}) \) \( 2q - 2q^{25} - 2q^{49} + 4q^{61} - 4q^{85} + O(q^{100}) \)

Character values

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

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

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 \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1279.1
1.00000i
1.00000i
0 0 0 1.00000i 0 0 0 0 0
1279.2 0 0 0 1.00000i 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 \(\Q(\sqrt{-1}) \)
15.d odd 2 1 CM by \(\Q(\sqrt{-15}) \)
60.h even 2 1 RM by \(\Q(\sqrt{15}) \)
3.b odd 2 1 inner
5.b even 2 1 inner
12.b even 2 1 inner
20.d odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2880.1.j.b 2
3.b odd 2 1 inner 2880.1.j.b 2
4.b odd 2 1 CM 2880.1.j.b 2
5.b even 2 1 inner 2880.1.j.b 2
8.b even 2 1 180.1.f.a 2
8.d odd 2 1 180.1.f.a 2
12.b even 2 1 inner 2880.1.j.b 2
15.d odd 2 1 CM 2880.1.j.b 2
20.d odd 2 1 inner 2880.1.j.b 2
24.f even 2 1 180.1.f.a 2
24.h odd 2 1 180.1.f.a 2
40.e odd 2 1 180.1.f.a 2
40.f even 2 1 180.1.f.a 2
40.i odd 4 1 900.1.c.a 1
40.i odd 4 1 900.1.c.b 1
40.k even 4 1 900.1.c.a 1
40.k even 4 1 900.1.c.b 1
60.h even 2 1 RM 2880.1.j.b 2
72.j odd 6 2 1620.1.p.b 4
72.l even 6 2 1620.1.p.b 4
72.n even 6 2 1620.1.p.b 4
72.p odd 6 2 1620.1.p.b 4
120.i odd 2 1 180.1.f.a 2
120.m even 2 1 180.1.f.a 2
120.q odd 4 1 900.1.c.a 1
120.q odd 4 1 900.1.c.b 1
120.w even 4 1 900.1.c.a 1
120.w even 4 1 900.1.c.b 1
360.z odd 6 2 1620.1.p.b 4
360.bd even 6 2 1620.1.p.b 4
360.bh odd 6 2 1620.1.p.b 4
360.bk even 6 2 1620.1.p.b 4
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
180.1.f.a 2 8.b even 2 1
180.1.f.a 2 8.d odd 2 1
180.1.f.a 2 24.f even 2 1
180.1.f.a 2 24.h odd 2 1
180.1.f.a 2 40.e odd 2 1
180.1.f.a 2 40.f even 2 1
180.1.f.a 2 120.i odd 2 1
180.1.f.a 2 120.m even 2 1
900.1.c.a 1 40.i odd 4 1
900.1.c.a 1 40.k even 4 1
900.1.c.a 1 120.q odd 4 1
900.1.c.a 1 120.w even 4 1
900.1.c.b 1 40.i odd 4 1
900.1.c.b 1 40.k even 4 1
900.1.c.b 1 120.q odd 4 1
900.1.c.b 1 120.w even 4 1
1620.1.p.b 4 72.j odd 6 2
1620.1.p.b 4 72.l even 6 2
1620.1.p.b 4 72.n even 6 2
1620.1.p.b 4 72.p odd 6 2
1620.1.p.b 4 360.z odd 6 2
1620.1.p.b 4 360.bd even 6 2
1620.1.p.b 4 360.bh odd 6 2
1620.1.p.b 4 360.bk even 6 2
2880.1.j.b 2 1.a even 1 1 trivial
2880.1.j.b 2 3.b odd 2 1 inner
2880.1.j.b 2 4.b odd 2 1 CM
2880.1.j.b 2 5.b even 2 1 inner
2880.1.j.b 2 12.b even 2 1 inner
2880.1.j.b 2 15.d odd 2 1 CM
2880.1.j.b 2 20.d odd 2 1 inner
2880.1.j.b 2 60.h even 2 1 RM

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{17}^{2} + 4 \) acting on \(S_{1}^{\mathrm{new}}(2880, [\chi])\).

Hecke Characteristic Polynomials

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