Newform orbit 1960.1.i.c

• Label: 1960.1.i.c
• Level: $1960$
• Weight: $1$
• Character orbit: 1960.i
• Self dual: yes
• Analytic conductor: $0.978$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -40
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1960.i (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(0.978167424761\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 280)
Projective image:	\(D_{3}\)
Projective field:	Galois closure of 3.1.1960.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.0.26891200.1

$q$-expansion

\(f(q)\)

\(=\)

\( q + q^{2} + q^{4} - q^{5} + q^{8} + q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1960\mathbb{Z}\right)^\times\).

\(n\)	\(981\)	\(1081\)	\(1177\)	\(1471\)
\(\chi(n)\)	\(-1\)	\(1\)	\(-1\)	\(-1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

99.1

0

1.00000

0

1.00000

−1.00000

0

0

1.00000

1.00000

−1.00000

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
40.e	odd	2	1	CM by \(\Q(\sqrt{-10}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1960.1.i.c		1
5.b	even	2	1		1960.1.i.b		1
7.b	odd	2	1		1960.1.i.d		1
7.c	even	3	2		1960.1.bi.a		2
7.d	odd	6	2		280.1.bi.a	✓	2
8.d	odd	2	1		1960.1.i.b		1
21.g	even	6	2		2520.1.ef.b		2
28.f	even	6	2		1120.1.by.a		2
35.c	odd	2	1		1960.1.i.a		1
35.i	odd	6	2		280.1.bi.b	yes	2
35.j	even	6	2		1960.1.bi.b		2
35.k	even	12	4		1400.1.ba.a		4
40.e	odd	2	1	CM	1960.1.i.c		1
56.e	even	2	1		1960.1.i.a		1
56.j	odd	6	2		1120.1.by.b		2
56.k	odd	6	2		1960.1.bi.b		2
56.m	even	6	2		280.1.bi.b	yes	2
105.p	even	6	2		2520.1.ef.a		2
140.s	even	6	2		1120.1.by.b		2
168.be	odd	6	2		2520.1.ef.a		2
280.n	even	2	1		1960.1.i.d		1
280.ba	even	6	2		280.1.bi.a	✓	2
280.bi	odd	6	2		1960.1.bi.a		2
280.bk	odd	6	2		1120.1.by.a		2
280.bp	odd	12	4		1400.1.ba.a		4
840.ct	odd	6	2		2520.1.ef.b		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
280.1.bi.a	✓	2	7.d	odd	6	2
280.1.bi.a	✓	2	280.ba	even	6	2
280.1.bi.b	yes	2	35.i	odd	6	2
280.1.bi.b	yes	2	56.m	even	6	2
1120.1.by.a		2	28.f	even	6	2
1120.1.by.a		2	280.bk	odd	6	2
1120.1.by.b		2	56.j	odd	6	2
1120.1.by.b		2	140.s	even	6	2
1400.1.ba.a		4	35.k	even	12	4
1400.1.ba.a		4	280.bp	odd	12	4
1960.1.i.a		1	35.c	odd	2	1
1960.1.i.a		1	56.e	even	2	1
1960.1.i.b		1	5.b	even	2	1
1960.1.i.b		1	8.d	odd	2	1
1960.1.i.c		1	1.a	even	1	1	trivial
1960.1.i.c		1	40.e	odd	2	1	CM
1960.1.i.d		1	7.b	odd	2	1
1960.1.i.d		1	280.n	even	2	1
1960.1.bi.a		2	7.c	even	3	2
1960.1.bi.a		2	280.bi	odd	6	2
1960.1.bi.b		2	35.j	even	6	2
1960.1.bi.b		2	56.k	odd	6	2
2520.1.ef.a		2	105.p	even	6	2
2520.1.ef.a		2	168.be	odd	6	2
2520.1.ef.b		2	21.g	even	6	2
2520.1.ef.b		2	840.ct	odd	6	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(1960, [\chi])\):

\( T_{13} - 1 \)

\( T_{19} - 1 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T - 1 \)
$3$	\( T \)
$5$	\( T + 1 \)
$7$	\( T \)
$11$	\( T + 1 \)