Newform orbit 2592.2.i.w

• Label: 2592.2.i.w
• Level: $2592$
• Weight: $2$
• Character orbit: 2592.i
• Analytic conductor: $20.697$
• Analytic rank: $0$
• Dimension: $2$
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2592 = 2^{5} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2592.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(20.6972242039\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{-3}) \)
Defining polynomial:	\( x^{2} - x + 1 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 96)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a primitive root of unity \(\zeta_{6}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	\( q + 2 \zeta_{6} q^{5} + ( - 4 \zeta_{6} + 4) q^{7}+O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{5} + 4 q^{7}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2592\mathbb{Z}\right)^\times\).

\(n\)	\(325\)	\(1217\)	\(2431\)
\(\chi(n)\)	\(1\)	\(-\zeta_{6}\)	\(1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

865.1

0.500000	+	0.866025i
0.500000	−	0.866025i

0

0

0

1.00000

+

1.73205i

0

2.00000

−

3.46410i

0

0

0

1729.1

0

0

0

1.00000

−

1.73205i

0

2.00000

+

3.46410i

0

0

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
9.c	even	3	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2592.2.i.w		2
3.b	odd	2	1		2592.2.i.h		2
4.b	odd	2	1		2592.2.i.q		2
9.c	even	3	1		288.2.a.b		1
9.c	even	3	1	inner	2592.2.i.w		2
9.d	odd	6	1		96.2.a.b	yes	1
9.d	odd	6	1		2592.2.i.h		2
12.b	even	2	1		2592.2.i.b		2
36.f	odd	6	1		288.2.a.c		1
36.f	odd	6	1		2592.2.i.q		2
36.h	even	6	1		96.2.a.a	✓	1
36.h	even	6	1		2592.2.i.b		2
45.h	odd	6	1		2400.2.a.q		1
45.j	even	6	1		7200.2.a.bx		1
45.k	odd	12	2		7200.2.f.f		2
45.l	even	12	2		2400.2.f.r		2
63.o	even	6	1		4704.2.a.e		1
72.j	odd	6	1		192.2.a.a		1
72.l	even	6	1		192.2.a.c		1
72.n	even	6	1		576.2.a.g		1
72.p	odd	6	1		576.2.a.h		1
144.u	even	12	2		768.2.d.a		2
144.v	odd	12	2		2304.2.d.c		2
144.w	odd	12	2		768.2.d.h		2
144.x	even	12	2		2304.2.d.s		2
180.n	even	6	1		2400.2.a.r		1
180.p	odd	6	1		7200.2.a.e		1
180.v	odd	12	2		2400.2.f.a		2
180.x	even	12	2		7200.2.f.x		2
252.s	odd	6	1		4704.2.a.t		1
360.bd	even	6	1		4800.2.a.f		1
360.bh	odd	6	1		4800.2.a.co		1
360.br	even	12	2		4800.2.f.e		2
360.bt	odd	12	2		4800.2.f.bh		2
504.cc	even	6	1		9408.2.a.ct		1
504.co	odd	6	1		9408.2.a.bj		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
96.2.a.a	✓	1	36.h	even	6	1
96.2.a.b	yes	1	9.d	odd	6	1
192.2.a.a		1	72.j	odd	6	1
192.2.a.c		1	72.l	even	6	1
288.2.a.b		1	9.c	even	3	1
288.2.a.c		1	36.f	odd	6	1
576.2.a.g		1	72.n	even	6	1
576.2.a.h		1	72.p	odd	6	1
768.2.d.a		2	144.u	even	12	2
768.2.d.h		2	144.w	odd	12	2
2304.2.d.c		2	144.v	odd	12	2
2304.2.d.s		2	144.x	even	12	2
2400.2.a.q		1	45.h	odd	6	1
2400.2.a.r		1	180.n	even	6	1
2400.2.f.a		2	180.v	odd	12	2
2400.2.f.r		2	45.l	even	12	2
2592.2.i.b		2	12.b	even	2	1
2592.2.i.b		2	36.h	even	6	1
2592.2.i.h		2	3.b	odd	2	1
2592.2.i.h		2	9.d	odd	6	1
2592.2.i.q		2	4.b	odd	2	1
2592.2.i.q		2	36.f	odd	6	1
2592.2.i.w		2	1.a	even	1	1	trivial
2592.2.i.w		2	9.c	even	3	1	inner
4704.2.a.e		1	63.o	even	6	1
4704.2.a.t		1	252.s	odd	6	1
4800.2.a.f		1	360.bd	even	6	1
4800.2.a.co		1	360.bh	odd	6	1
4800.2.f.e		2	360.br	even	12	2
4800.2.f.bh		2	360.bt	odd	12	2
7200.2.a.e		1	180.p	odd	6	1
7200.2.a.bx		1	45.j	even	6	1
7200.2.f.f		2	45.k	odd	12	2
7200.2.f.x		2	180.x	even	12	2
9408.2.a.bj		1	504.co	odd	6	1
9408.2.a.ct		1	504.cc	even	6	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(2592, [\chi])\):

\( T_{5}^{2} - 2T_{5} + 4 \)

\( T_{7}^{2} - 4T_{7} + 16 \)

\( T_{11}^{2} - 4T_{11} + 16 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( T^{2} \)
$5$	\( T^{2} - 2T + 4 \)
$7$	\( T^{2} - 4T + 16 \)
$11$	\( T^{2} - 4T + 16 \)