Newform orbit 1470.2.a.o

• Label: 1470.2.a.o
• Level: $1470$
• Weight: $2$
• Character orbit: 1470.a
• Self dual: yes
• Analytic conductor: $11.738$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(11.7380090971\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 210)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

q + q^2 + q^3 + q^4 - q^5 + q^6 + q^8 + q^9 - q^10 - 5 * q^11 + q^12 + 5 * q^13 - q^15 + q^16 + 4 * q^17 + q^18 + 7 * q^19 - q^20 - 5 * q^22 + q^23 + q^24 + q^25 + 5 * q^26 + q^27 - q^30 + 2 * q^31 + q^32 - 5 * q^33 + 4 * q^34 + q^36 + q^37 + 7 * q^38 + 5 * q^39 - q^40 - 5 * q^41 + 12 * q^43 - 5 * q^44 - q^45 + q^46 + 11 * q^47 + q^48 + q^50 + 4 * q^51 + 5 * q^52 - 9 * q^53 + q^54 + 5 * q^55 + 7 * q^57 - 4 * q^59 - q^60 - 4 * q^61 + 2 * q^62 + q^64 - 5 * q^65 - 5 * q^66 - 12 * q^67 + 4 * q^68 + q^69 + 2 * q^71 + q^72 - 10 * q^73 + q^74 + q^75 + 7 * q^76 + 5 * q^78 - 12 * q^79 - q^80 + q^81 - 5 * q^82 + 12 * q^83 - 4 * q^85 + 12 * q^86 - 5 * q^88 - 14 * q^89 - q^90 + q^92 + 2 * q^93 + 11 * q^94 - 7 * q^95 + q^96 + 8 * q^97 - 5 * q^99

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1.1

0

1.00000

1.00000

1.00000

−1.00000

1.00000

0

1.00000

1.00000

−1.00000

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( -1 \)
\(3\)	\( -1 \)
\(5\)	\( +1 \)
\(7\)	\( -1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1470.2.a.o		1
3.b	odd	2	1		4410.2.a.u		1
5.b	even	2	1		7350.2.a.a		1
7.b	odd	2	1		1470.2.a.l		1
7.c	even	3	2		1470.2.i.e		2
7.d	odd	6	2		210.2.i.b	✓	2
21.c	even	2	1		4410.2.a.j		1
21.g	even	6	2		630.2.k.g		2
28.f	even	6	2		1680.2.bg.d		2
35.c	odd	2	1		7350.2.a.u		1
35.i	odd	6	2		1050.2.i.p		2
35.k	even	12	4		1050.2.o.g		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
210.2.i.b	✓	2	7.d	odd	6	2
630.2.k.g		2	21.g	even	6	2
1050.2.i.p		2	35.i	odd	6	2
1050.2.o.g		4	35.k	even	12	4
1470.2.a.l		1	7.b	odd	2	1
1470.2.a.o		1	1.a	even	1	1	trivial
1470.2.i.e		2	7.c	even	3	2
1680.2.bg.d		2	28.f	even	6	2
4410.2.a.j		1	21.c	even	2	1
4410.2.a.u		1	3.b	odd	2	1
7350.2.a.a		1	5.b	even	2	1
7350.2.a.u		1	35.c	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(1470))\):

\( T_{11} + 5 \)

\( T_{13} - 5 \)

\( T_{17} - 4 \)

\( T_{19} - 7 \)

\( T_{31} - 2 \)

Hecke characteristic polynomials

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