Newform orbit 3600.2.a.q

• Label: 3600.2.a.q
• Level: $3600$
• Weight: $2$
• Character orbit: 3600.a
• Self dual: yes
• Analytic conductor: $28.746$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -3
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$3600 = 2^{4} \cdot 3^{2} \cdot 5^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	3600.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$28.7461447277$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 900)
Fricke sign:	$-1$
Sato-Tate group:	$N(\mathrm{U}(1))$

$q$-expansion

$f(q)$

$=$

$q - q^{7} + 7 q^{13} + 7 q^{19} - 11 q^{31} + 10 q^{37} - 13 q^{43} - 6 q^{49} - q^{61} + 11 q^{67} + 10 q^{73} + 4 q^{79} - 7 q^{91} + 19 q^{97}+O(q^{100})$

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

0

0

−1.00000

0

0

0

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$3$	$+1$
$5$	$+1$

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	CM by $\Q(\sqrt{-3})$

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	3600.2.a.q		1
3.b	odd	2	1	CM	3600.2.a.q		1
4.b	odd	2	1		900.2.a.f	yes	1
5.b	even	2	1		3600.2.a.x		1
5.c	odd	4	2		3600.2.f.h		2
12.b	even	2	1		900.2.a.f	yes	1
15.d	odd	2	1		3600.2.a.x		1
15.e	even	4	2		3600.2.f.h		2
20.d	odd	2	1		900.2.a.d	✓	1
20.e	even	4	2		900.2.d.d		2
60.h	even	2	1		900.2.a.d	✓	1
60.l	odd	4	2		900.2.d.d		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
900.2.a.d	✓	1	20.d	odd	2	1
900.2.a.d	✓	1	60.h	even	2	1
900.2.a.f	yes	1	4.b	odd	2	1
900.2.a.f	yes	1	12.b	even	2	1
900.2.d.d		2	20.e	even	4	2
900.2.d.d		2	60.l	odd	4	2
3600.2.a.q		1	1.a	even	1	1	trivial
3600.2.a.q		1	3.b	odd	2	1	CM
3600.2.a.x		1	5.b	even	2	1
3600.2.a.x		1	15.d	odd	2	1
3600.2.f.h		2	5.c	odd	4	2
3600.2.f.h		2	15.e	even	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(\Gamma_0(3600))$:

$T_{7} + 1$

$T_{11}$

$T_{13} - 7$

$T_{17}$

Hecke characteristic polynomials

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