Newform orbit 3528.2.a.ba

• Label: 3528.2.a.ba
• Level: $3528$
• Weight: $2$
• Character orbit: 3528.a
• Self dual: yes
• Analytic conductor: $28.171$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$3528 = 2^{3} \cdot 3^{2} \cdot 7^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3528.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$28.1712218331$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 504)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q + 4 * q^5 + 3 * q^13 - 4 * q^17 - 7 * q^19 - 4 * q^23 + 11 * q^25 + 8 * q^29 + 5 * q^31 + 3 * q^37 + 8 * q^41 + 11 * q^43 + 4 * q^47 - 4 * q^53 + 12 * q^59 + 2 * q^61 + 12 * q^65 - 3 * q^67 - 12 * q^71 - q^73 + q^79 + 12 * q^83 - 16 * q^85 + 8 * q^89 - 28 * q^95 + 2 * q^97

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

0

0

0

4.00000

0

0

0

0

0

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$3$	$+1$
$7$	$-1$

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	3528.2.a.ba		1
3.b	odd	2	1		3528.2.a.c		1
4.b	odd	2	1		7056.2.a.cc		1
7.b	odd	2	1		3528.2.a.a		1
7.c	even	3	2		3528.2.s.b		2
7.d	odd	6	2		504.2.s.h	yes	2
12.b	even	2	1		7056.2.a.d		1
21.c	even	2	1		3528.2.a.z		1
21.g	even	6	2		504.2.s.a	✓	2
21.h	odd	6	2		3528.2.s.bb		2
28.d	even	2	1		7056.2.a.b		1
28.f	even	6	2		1008.2.s.q		2
84.h	odd	2	1		7056.2.a.cb		1
84.j	odd	6	2		1008.2.s.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
504.2.s.a	✓	2	21.g	even	6	2
504.2.s.h	yes	2	7.d	odd	6	2
1008.2.s.a		2	84.j	odd	6	2
1008.2.s.q		2	28.f	even	6	2
3528.2.a.a		1	7.b	odd	2	1
3528.2.a.c		1	3.b	odd	2	1
3528.2.a.z		1	21.c	even	2	1
3528.2.a.ba		1	1.a	even	1	1	trivial
3528.2.s.b		2	7.c	even	3	2
3528.2.s.bb		2	21.h	odd	6	2
7056.2.a.b		1	28.d	even	2	1
7056.2.a.d		1	12.b	even	2	1
7056.2.a.cb		1	84.h	odd	2	1
7056.2.a.cc		1	4.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(3528))$:

$T_{5} - 4$

$T_{11}$

$T_{13} - 3$

$T_{23} + 4$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T$
$5$	$T - 4$
$7$	$T$
$11$	$T$