Newform orbit 2900.1.g.a

• Label: 2900.1.g.a
• Level: $2900$
• Weight: $1$
• Character orbit: 2900.g
• Self dual: yes
• Analytic conductor: $1.447$
• Analytic rank: $0$
• Dimension: $1$
• Projective image: $D_{3}$
• CM discriminant: -116
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2900.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	\(1.44728853664\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 116)
Projective image:	\(D_{3}\)
Projective field:	Galois closure of 3.1.116.1
Artin image:	$D_6$
Artin field:	Galois closure of 6.2.1682000.1

$q$-expansion

\(f(q)\)

\(=\)

\( q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2900\mathbb{Z}\right)^\times\).

\(n\)	\(901\)	\(1277\)	\(1451\)
\(\chi(n)\)	\(-1\)	\(1\)	\(-1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

2551.1

0

−1.00000

1.00000

1.00000

0

−1.00000

0

−1.00000

0

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
116.d	odd	2	1	CM by \(\Q(\sqrt{-29}) \)

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2900.1.g.a		1
4.b	odd	2	1		2900.1.g.d		1
5.b	even	2	1		116.1.d.b	yes	1
5.c	odd	4	2		2900.1.e.a		2
15.d	odd	2	1		1044.1.g.a		1
20.d	odd	2	1		116.1.d.a	✓	1
20.e	even	4	2		2900.1.e.b		2
29.b	even	2	1		2900.1.g.d		1
40.e	odd	2	1		1856.1.h.a		1
40.f	even	2	1		1856.1.h.c		1
60.h	even	2	1		1044.1.g.b		1
116.d	odd	2	1	CM	2900.1.g.a		1
145.d	even	2	1		116.1.d.a	✓	1
145.f	odd	4	2		3364.1.b.a		2
145.h	odd	4	2		2900.1.e.b		2
145.l	even	14	6		3364.1.h.b		6
145.n	even	14	6		3364.1.h.a		6
145.s	odd	28	12		3364.1.j.f		12
435.b	odd	2	1		1044.1.g.b		1
580.e	odd	2	1		116.1.d.b	yes	1
580.o	even	4	2		2900.1.e.a		2
580.r	even	4	2		3364.1.b.a		2
580.v	odd	14	6		3364.1.h.b		6
580.y	odd	14	6		3364.1.h.a		6
580.be	even	28	12		3364.1.j.f		12
1160.e	even	2	1		1856.1.h.a		1
1160.o	odd	2	1		1856.1.h.c		1
1740.k	even	2	1		1044.1.g.a		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
116.1.d.a	✓	1	20.d	odd	2	1
116.1.d.a	✓	1	145.d	even	2	1
116.1.d.b	yes	1	5.b	even	2	1
116.1.d.b	yes	1	580.e	odd	2	1
1044.1.g.a		1	15.d	odd	2	1
1044.1.g.a		1	1740.k	even	2	1
1044.1.g.b		1	60.h	even	2	1
1044.1.g.b		1	435.b	odd	2	1
1856.1.h.a		1	40.e	odd	2	1
1856.1.h.a		1	1160.e	even	2	1
1856.1.h.c		1	40.f	even	2	1
1856.1.h.c		1	1160.o	odd	2	1
2900.1.e.a		2	5.c	odd	4	2
2900.1.e.a		2	580.o	even	4	2
2900.1.e.b		2	20.e	even	4	2
2900.1.e.b		2	145.h	odd	4	2
2900.1.g.a		1	1.a	even	1	1	trivial
2900.1.g.a		1	116.d	odd	2	1	CM
2900.1.g.d		1	4.b	odd	2	1
2900.1.g.d		1	29.b	even	2	1
3364.1.b.a		2	145.f	odd	4	2
3364.1.b.a		2	580.r	even	4	2
3364.1.h.a		6	145.n	even	14	6
3364.1.h.a		6	580.y	odd	14	6
3364.1.h.b		6	145.l	even	14	6
3364.1.h.b		6	580.v	odd	14	6
3364.1.j.f		12	145.s	odd	28	12
3364.1.j.f		12	580.be	even	28	12

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{1}^{\mathrm{new}}(2900, [\chi])\):

\( T_{3} - 1 \)

\( T_{11} + 1 \)

Hecke characteristic polynomials

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