Newform orbit 1920.2.y.b

• Label: 1920.2.y.b
• Level: $1920$
• Weight: $2$
• Character orbit: 1920.y
• Analytic conductor: $15.331$
• Analytic rank: $1$
• Dimension: $2$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.y (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(15.3312771881\)
Analytic rank:	\(1\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{-1}) \)
Defining polynomial:	\( x^{2} + 1 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(i = \sqrt{-1}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	\( q - q^{3} + (2 i + 1) q^{5} + (i + 1) q^{7} + q^{9}+O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 2 q^{5} + 2 q^{7} + 2 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1920\mathbb{Z}\right)^\times\).

\(n\)	\(511\)	\(641\)	\(901\)	\(1537\)
\(\chi(n)\)	\(-1\)	\(1\)	\(i\)	\(i\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

223.1

	−	1.00000i
		1.00000i

0

−1.00000

0

1.00000

−

2.00000i

0

1.00000

−

1.00000i

0

1.00000

0

1567.1

0

−1.00000

0

1.00000

+

2.00000i

0

1.00000

+

1.00000i

0

1.00000

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
80.s	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1920.2.y.b		2
4.b	odd	2	1		1920.2.y.f		2
5.c	odd	4	1		1920.2.bc.d		2
8.b	even	2	1		960.2.y.b		2
8.d	odd	2	1		240.2.y.a	✓	2
16.e	even	4	1		240.2.bc.b	yes	2
16.e	even	4	1		1920.2.bc.c		2
16.f	odd	4	1		960.2.bc.c		2
16.f	odd	4	1		1920.2.bc.d		2
20.e	even	4	1		1920.2.bc.c		2
24.f	even	2	1		720.2.z.b		2
40.i	odd	4	1		960.2.bc.c		2
40.k	even	4	1		240.2.bc.b	yes	2
48.i	odd	4	1		720.2.bd.c		2
80.i	odd	4	1		1920.2.y.f		2
80.j	even	4	1		960.2.y.b		2
80.s	even	4	1	inner	1920.2.y.b		2
80.t	odd	4	1		240.2.y.a	✓	2
120.q	odd	4	1		720.2.bd.c		2
240.bf	even	4	1		720.2.z.b		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
240.2.y.a	✓	2	8.d	odd	2	1
240.2.y.a	✓	2	80.t	odd	4	1
240.2.bc.b	yes	2	16.e	even	4	1
240.2.bc.b	yes	2	40.k	even	4	1
720.2.z.b		2	24.f	even	2	1
720.2.z.b		2	240.bf	even	4	1
720.2.bd.c		2	48.i	odd	4	1
720.2.bd.c		2	120.q	odd	4	1
960.2.y.b		2	8.b	even	2	1
960.2.y.b		2	80.j	even	4	1
960.2.bc.c		2	16.f	odd	4	1
960.2.bc.c		2	40.i	odd	4	1
1920.2.y.b		2	1.a	even	1	1	trivial
1920.2.y.b		2	80.s	even	4	1	inner
1920.2.y.f		2	4.b	odd	2	1
1920.2.y.f		2	80.i	odd	4	1
1920.2.bc.c		2	16.e	even	4	1
1920.2.bc.c		2	20.e	even	4	1
1920.2.bc.d		2	5.c	odd	4	1
1920.2.bc.d		2	16.f	odd	4	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1920, [\chi])\):

\( T_{7}^{2} - 2T_{7} + 2 \)

\( T_{11}^{2} + 6T_{11} + 18 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( (T + 1)^{2} \)
$5$	\( T^{2} - 2T + 5 \)
$7$	\( T^{2} - 2T + 2 \)
$11$	\( T^{2} + 6T + 18 \)