Newform orbit 1520.1.m.c

• Label: 1520.1.m.c
• Level: $1520$
• Weight: $1$
• Character orbit: 1520.m
• Analytic conductor: $0.759$
• Analytic rank: $0$
• Dimension: $2$
• Projective image: $D_{6}$
• CM discriminant: -19
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1520.m (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(0.758578819202\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\zeta_{6})\)
Defining polynomial:	\( x^{2} - x + 1 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 380)
Projective image:	\(D_{6}\)
Projective field:	Galois closure of 6.2.722000.1

$q$-expansion

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

\(f(q)\)	\(=\)	q - z * q^5 + (z^2 + z) * q^7 - q^9 - q^11 + (z^2 + z) * q^17 - q^19 + z^2 * q^25 + (-z^2 + 1) * q^35 + (z^2 + z) * q^43 + z * q^45 + (-z^2 - z) * q^47 + (z^2 - z - 1) * q^49 + z * q^55 + q^61 + (-z^2 - z) * q^63 + (z^2 + z) * q^73 + (-z^2 - z) * q^77 + q^81 + (-z^2 + 1) * q^85 + z * q^95 + q^99
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{5} - 2 q^{9} - 2 q^{11} - 2 q^{19} - q^{25} + 3 q^{35} + q^{45} - 4 q^{49} + q^{55} + 2 q^{61} + 2 q^{81} + 3 q^{85} + q^{95} + 2 q^{99}+O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).

\(n\)	\(191\)	\(401\)	\(1141\)	\(1217\)
\(\chi(n)\)	\(1\)	\(-1\)	\(1\)	\(-1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1329.1

0.500000	+	0.866025i
0.500000	−	0.866025i

0

0

0

−0.500000

−

0.866025i

0

1.73205i

0

−1.00000

0

1329.2

0

0

0

−0.500000

+

0.866025i

0

−

1.73205i

0

−1.00000

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
19.b	odd	2	1	CM by \(\Q(\sqrt{-19}) \)
5.b	even	2	1	inner
95.d	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1520.1.m.c		2
4.b	odd	2	1		380.1.g.a	✓	2
5.b	even	2	1	inner	1520.1.m.c		2
12.b	even	2	1		3420.1.h.a		2
19.b	odd	2	1	CM	1520.1.m.c		2
20.d	odd	2	1		380.1.g.a	✓	2
20.e	even	4	2		1900.1.e.b		2
60.h	even	2	1		3420.1.h.a		2
76.d	even	2	1		380.1.g.a	✓	2
95.d	odd	2	1	inner	1520.1.m.c		2
228.b	odd	2	1		3420.1.h.a		2
380.d	even	2	1		380.1.g.a	✓	2
380.j	odd	4	2		1900.1.e.b		2
1140.p	odd	2	1		3420.1.h.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
380.1.g.a	✓	2	4.b	odd	2	1
380.1.g.a	✓	2	20.d	odd	2	1
380.1.g.a	✓	2	76.d	even	2	1
380.1.g.a	✓	2	380.d	even	2	1
1520.1.m.c		2	1.a	even	1	1	trivial
1520.1.m.c		2	5.b	even	2	1	inner
1520.1.m.c		2	19.b	odd	2	1	CM
1520.1.m.c		2	95.d	odd	2	1	inner
1900.1.e.b		2	20.e	even	4	2
1900.1.e.b		2	380.j	odd	4	2
3420.1.h.a		2	12.b	even	2	1
3420.1.h.a		2	60.h	even	2	1
3420.1.h.a		2	228.b	odd	2	1
3420.1.h.a		2	1140.p	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(1520, [\chi])\):

\( T_{3} \)

\( T_{7}^{2} + 3 \)

Hecke characteristic polynomials

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