Newform orbit 1100.1.f.a

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

Newspace parameters

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1100.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(0.548971513896\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
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:	$D_6$
Artin field:	Galois closure of 6.2.242000.1
Stark unit:	Root of $x^{6} - 1376x^{5} + 9595x^{4} - 1876940x^{3} + 9595x^{2} - 1376x + 1$

$q$-expansion

\(f(q)\)

\(=\)

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

Character values

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

\(n\)	\(101\)	\(177\)	\(551\)
\(\chi(n)\)	\(1\)	\(0\)	\(0\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

901.1

0

0

1.00000

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 \(\Q(\sqrt{-11}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1100.1.f.a		1
5.b	even	2	1		44.1.d.a	✓	1
5.c	odd	4	2		1100.1.e.a		2
11.b	odd	2	1	CM	1100.1.f.a		1
15.d	odd	2	1		396.1.f.a		1
20.d	odd	2	1		176.1.h.a		1
35.c	odd	2	1		2156.1.h.a		1
35.i	odd	6	2		2156.1.k.a		2
35.j	even	6	2		2156.1.k.b		2
40.e	odd	2	1		704.1.h.a		1
40.f	even	2	1		704.1.h.b		1
45.h	odd	6	2		3564.1.m.a		2
45.j	even	6	2		3564.1.m.b		2
55.d	odd	2	1		44.1.d.a	✓	1
55.e	even	4	2		1100.1.e.a		2
55.h	odd	10	4		484.1.f.a		4
55.j	even	10	4		484.1.f.a		4
60.h	even	2	1		1584.1.j.a		1
80.k	odd	4	2		2816.1.b.a		2
80.q	even	4	2		2816.1.b.b		2
165.d	even	2	1		396.1.f.a		1
220.g	even	2	1		176.1.h.a		1
220.n	odd	10	4		1936.1.n.a		4
220.o	even	10	4		1936.1.n.a		4
385.h	even	2	1		2156.1.h.a		1
385.o	even	6	2		2156.1.k.a		2
385.q	odd	6	2		2156.1.k.b		2
440.c	even	2	1		704.1.h.a		1
440.o	odd	2	1		704.1.h.b		1
495.o	odd	6	2		3564.1.m.b		2
495.r	even	6	2		3564.1.m.a		2
660.g	odd	2	1		1584.1.j.a		1
880.x	odd	4	2		2816.1.b.b		2
880.bi	even	4	2		2816.1.b.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
44.1.d.a	✓	1	5.b	even	2	1
44.1.d.a	✓	1	55.d	odd	2	1
176.1.h.a		1	20.d	odd	2	1
176.1.h.a		1	220.g	even	2	1
396.1.f.a		1	15.d	odd	2	1
396.1.f.a		1	165.d	even	2	1
484.1.f.a		4	55.h	odd	10	4
484.1.f.a		4	55.j	even	10	4
704.1.h.a		1	40.e	odd	2	1
704.1.h.a		1	440.c	even	2	1
704.1.h.b		1	40.f	even	2	1
704.1.h.b		1	440.o	odd	2	1
1100.1.e.a		2	5.c	odd	4	2
1100.1.e.a		2	55.e	even	4	2
1100.1.f.a		1	1.a	even	1	1	trivial
1100.1.f.a		1	11.b	odd	2	1	CM
1584.1.j.a		1	60.h	even	2	1
1584.1.j.a		1	660.g	odd	2	1
1936.1.n.a		4	220.n	odd	10	4
1936.1.n.a		4	220.o	even	10	4
2156.1.h.a		1	35.c	odd	2	1
2156.1.h.a		1	385.h	even	2	1
2156.1.k.a		2	35.i	odd	6	2
2156.1.k.a		2	385.o	even	6	2
2156.1.k.b		2	35.j	even	6	2
2156.1.k.b		2	385.q	odd	6	2
2816.1.b.a		2	80.k	odd	4	2
2816.1.b.a		2	880.bi	even	4	2
2816.1.b.b		2	80.q	even	4	2
2816.1.b.b		2	880.x	odd	4	2
3564.1.m.a		2	45.h	odd	6	2
3564.1.m.a		2	495.r	even	6	2
3564.1.m.b		2	45.j	even	6	2
3564.1.m.b		2	495.o	odd	6	2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} - 1 \) acting on \(S_{1}^{\mathrm{new}}(1100, [\chi])\).

Hecke characteristic polynomials

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