Newform orbit 1100.1.e.a

• Label: 1100.1.e.a
• Level: $1100$
• Weight: $1$
• Character orbit: 1100.e
• Analytic conductor: $0.549$
• Analytic rank: $0$
• Dimension: $2$
• Projective image: $D_{3}$
• CM discriminant: -11
• Inner twists: $4$

Newspace parameters

Level:	$N$	$=$	$1100 = 2^{2} \cdot 5^{2} \cdot 11$
Weight:	$k$	$=$	$1$
Character orbit:	$[\chi]$	$=$	1100.e (of order $2$, degree $1$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$0.548971513896$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
Defining polynomial:	$x^{2} + 1$
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 44)
Projective image:	$D_{3}$
Projective field:	Galois closure of 3.1.44.1
Artin image:	$C_4\times S_3$
Artin field:	Galois closure of 12.0.7320500000000.2

$q$-expansion

The $q$-expansion and trace form are shown below.

$f(q)$	$=$	$q - i q^{3} + q^{11} - i q^{23} - i q^{27} - q^{31} - i q^{33} + i q^{37} - 2 i q^{47} - q^{49} + 2 i q^{53} + q^{59} + i q^{67} - q^{69} - q^{71} - q^{81} + q^{89} + i q^{93} + i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q + 2 q^{11} - 2 q^{31} - 2 q^{49} + 2 q^{59} - 2 q^{69} - 2 q^{71} - 2 q^{81} + 2 q^{89}+O(q^{100})$

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$-1$	$-1$	$1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

549.1

		1.00000i
	−	1.00000i

0

−

1.00000i

0

0

0

0

0

0

0

549.2

0

1.00000i

0

0

0

0

0

0

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
11.b	odd	2	1	CM by $\Q(\sqrt{-11})$
5.b	even	2	1	inner
55.d	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1100.1.e.a		2
5.b	even	2	1	inner	1100.1.e.a		2
5.c	odd	4	1		44.1.d.a	✓	1
5.c	odd	4	1		1100.1.f.a		1
11.b	odd	2	1	CM	1100.1.e.a		2
15.e	even	4	1		396.1.f.a		1
20.e	even	4	1		176.1.h.a		1
35.f	even	4	1		2156.1.h.a		1
35.k	even	12	2		2156.1.k.a		2
35.l	odd	12	2		2156.1.k.b		2
40.i	odd	4	1		704.1.h.b		1
40.k	even	4	1		704.1.h.a		1
45.k	odd	12	2		3564.1.m.b		2
45.l	even	12	2		3564.1.m.a		2
55.d	odd	2	1	inner	1100.1.e.a		2
55.e	even	4	1		44.1.d.a	✓	1
55.e	even	4	1		1100.1.f.a		1
55.k	odd	20	4		484.1.f.a		4
55.l	even	20	4		484.1.f.a		4
60.l	odd	4	1		1584.1.j.a		1
80.i	odd	4	1		2816.1.b.b		2
80.j	even	4	1		2816.1.b.a		2
80.s	even	4	1		2816.1.b.a		2
80.t	odd	4	1		2816.1.b.b		2
165.l	odd	4	1		396.1.f.a		1
220.i	odd	4	1		176.1.h.a		1
220.v	even	20	4		1936.1.n.a		4
220.w	odd	20	4		1936.1.n.a		4
385.l	odd	4	1		2156.1.h.a		1
385.bc	even	12	2		2156.1.k.b		2
385.bf	odd	12	2		2156.1.k.a		2
440.t	even	4	1		704.1.h.b		1
440.w	odd	4	1		704.1.h.a		1
495.bd	odd	12	2		3564.1.m.a		2
495.bf	even	12	2		3564.1.m.b		2
660.q	even	4	1		1584.1.j.a		1
880.q	odd	4	1		2816.1.b.a		2
880.t	even	4	1		2816.1.b.b		2
880.bl	even	4	1		2816.1.b.b		2
880.bm	odd	4	1		2816.1.b.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
44.1.d.a	✓	1	5.c	odd	4	1
44.1.d.a	✓	1	55.e	even	4	1
176.1.h.a		1	20.e	even	4	1
176.1.h.a		1	220.i	odd	4	1
396.1.f.a		1	15.e	even	4	1
396.1.f.a		1	165.l	odd	4	1
484.1.f.a		4	55.k	odd	20	4
484.1.f.a		4	55.l	even	20	4
704.1.h.a		1	40.k	even	4	1
704.1.h.a		1	440.w	odd	4	1
704.1.h.b		1	40.i	odd	4	1
704.1.h.b		1	440.t	even	4	1
1100.1.e.a		2	1.a	even	1	1	trivial
1100.1.e.a		2	5.b	even	2	1	inner
1100.1.e.a		2	11.b	odd	2	1	CM
1100.1.e.a		2	55.d	odd	2	1	inner
1100.1.f.a		1	5.c	odd	4	1
1100.1.f.a		1	55.e	even	4	1
1584.1.j.a		1	60.l	odd	4	1
1584.1.j.a		1	660.q	even	4	1
1936.1.n.a		4	220.v	even	20	4
1936.1.n.a		4	220.w	odd	20	4
2156.1.h.a		1	35.f	even	4	1
2156.1.h.a		1	385.l	odd	4	1
2156.1.k.a		2	35.k	even	12	2
2156.1.k.a		2	385.bf	odd	12	2
2156.1.k.b		2	35.l	odd	12	2
2156.1.k.b		2	385.bc	even	12	2
2816.1.b.a		2	80.j	even	4	1
2816.1.b.a		2	80.s	even	4	1
2816.1.b.a		2	880.q	odd	4	1
2816.1.b.a		2	880.bm	odd	4	1
2816.1.b.b		2	80.i	odd	4	1
2816.1.b.b		2	80.t	odd	4	1
2816.1.b.b		2	880.t	even	4	1
2816.1.b.b		2	880.bl	even	4	1
3564.1.m.a		2	45.l	even	12	2
3564.1.m.a		2	495.bd	odd	12	2
3564.1.m.b		2	45.k	odd	12	2
3564.1.m.b		2	495.bf	even	12	2

Hecke kernels

This newform subspace is the entire newspace $S_{1}^{\mathrm{new}}(1100, [\chi])$.

Hecke characteristic polynomials

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