Newform orbit 2496.2.c.e

• Label: 2496.2.c.e
• Level: $2496$
• Weight: $2$
• Character orbit: 2496.c
• Analytic conductor: $19.931$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2496 = 2^{6} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2496.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(19.9306603445\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{-3}) \)
Defining polynomial:	\( x^{2} - x + 1 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index:	\( 2^{2} \)
Twist minimal:	no (minimal twist has level 156)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = 2\sqrt{-3}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	\( q - q^{3} - \beta q^{5} + q^{9} +O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 2 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2496\mathbb{Z}\right)^\times\).

\(n\)	\(703\)	\(769\)	\(833\)	\(1093\)
\(\chi(n)\)	\(1\)	\(-1\)	\(1\)	\(1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

961.1

0.500000	+	0.866025i
0.500000	−	0.866025i

0

−1.00000

0

−

3.46410i

0

0

0

1.00000

0

961.2

0

−1.00000

0

3.46410i

0

0

0

1.00000

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
13.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2496.2.c.e		2
4.b	odd	2	1		2496.2.c.l		2
8.b	even	2	1		624.2.c.f		2
8.d	odd	2	1		156.2.b.a	✓	2
13.b	even	2	1	inner	2496.2.c.e		2
24.f	even	2	1		468.2.b.a		2
24.h	odd	2	1		1872.2.c.c		2
40.e	odd	2	1		3900.2.c.c		2
40.k	even	4	2		3900.2.j.h		4
52.b	odd	2	1		2496.2.c.l		2
56.e	even	2	1		7644.2.e.g		2
104.e	even	2	1		624.2.c.f		2
104.h	odd	2	1		156.2.b.a	✓	2
104.j	odd	4	2		8112.2.a.bs		2
104.m	even	4	2		2028.2.a.g		2
104.n	odd	6	1		2028.2.q.b		2
104.n	odd	6	1		2028.2.q.c		2
104.p	odd	6	1		2028.2.q.b		2
104.p	odd	6	1		2028.2.q.c		2
104.u	even	12	4		2028.2.i.i		4
312.b	odd	2	1		1872.2.c.c		2
312.h	even	2	1		468.2.b.a		2
312.w	odd	4	2		6084.2.a.v		2
520.b	odd	2	1		3900.2.c.c		2
520.bc	even	4	2		3900.2.j.h		4
728.b	even	2	1		7644.2.e.g		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
156.2.b.a	✓	2	8.d	odd	2	1
156.2.b.a	✓	2	104.h	odd	2	1
468.2.b.a		2	24.f	even	2	1
468.2.b.a		2	312.h	even	2	1
624.2.c.f		2	8.b	even	2	1
624.2.c.f		2	104.e	even	2	1
1872.2.c.c		2	24.h	odd	2	1
1872.2.c.c		2	312.b	odd	2	1
2028.2.a.g		2	104.m	even	4	2
2028.2.i.i		4	104.u	even	12	4
2028.2.q.b		2	104.n	odd	6	1
2028.2.q.b		2	104.p	odd	6	1
2028.2.q.c		2	104.n	odd	6	1
2028.2.q.c		2	104.p	odd	6	1
2496.2.c.e		2	1.a	even	1	1	trivial
2496.2.c.e		2	13.b	even	2	1	inner
2496.2.c.l		2	4.b	odd	2	1
2496.2.c.l		2	52.b	odd	2	1
3900.2.c.c		2	40.e	odd	2	1
3900.2.c.c		2	520.b	odd	2	1
3900.2.j.h		4	40.k	even	4	2
3900.2.j.h		4	520.bc	even	4	2
6084.2.a.v		2	312.w	odd	4	2
7644.2.e.g		2	56.e	even	2	1
7644.2.e.g		2	728.b	even	2	1
8112.2.a.bs		2	104.j	odd	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(2496, [\chi])\):

\( T_{5}^{2} + 12 \)

\( T_{7} \)

\( T_{11}^{2} + 12 \)

\( T_{23} \)

\( T_{43} - 8 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( (T + 1)^{2} \)
$5$	\( T^{2} + 12 \)
$7$	\( T^{2} \)
$11$	\( T^{2} + 12 \)