Newform orbit 1911.2.c.d

• Label: 1911.2.c.d
• Level: $1911$
• Weight: $2$
• Character orbit: 1911.c
• Analytic conductor: $15.259$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1911 = 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1911.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(15.2594118263\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{-3}) \)
Defining polynomial:	\( x^{2} - x + 1 \)
Coefficient ring:	\(\Z[a_1, a_2]\)
Coefficient ring index:	\( 2 \)
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(f(q)\)	\(=\)	\( q - \beta q^{2} + q^{3} - q^{4} - \beta q^{6} - \beta q^{8} + q^{9} +O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} - 2 q^{4} + 2 q^{9}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1911\mathbb{Z}\right)^\times\).

\(n\)	\(638\)	\(1471\)	\(1522\)
\(\chi(n)\)	\(1\)	\(-1\)	\(1\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

883.1

0.500000	+	0.866025i
0.500000	−	0.866025i

−

1.73205i

1.00000

−1.00000

0

−

1.73205i

0

−

1.73205i

1.00000

0

883.2

1.73205i

1.00000

−1.00000

0

1.73205i

0

1.73205i

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	1911.2.c.d		2
7.b	odd	2	1		39.2.b.a	✓	2
13.b	even	2	1	inner	1911.2.c.d		2
21.c	even	2	1		117.2.b.a		2
28.d	even	2	1		624.2.c.e		2
35.c	odd	2	1		975.2.b.d		2
35.f	even	4	2		975.2.h.f		4
56.e	even	2	1		2496.2.c.d		2
56.h	odd	2	1		2496.2.c.k		2
84.h	odd	2	1		1872.2.c.e		2
91.b	odd	2	1		39.2.b.a	✓	2
91.i	even	4	2		507.2.a.f		2
91.n	odd	6	1		507.2.j.a		2
91.n	odd	6	1		507.2.j.c		2
91.t	odd	6	1		507.2.j.a		2
91.t	odd	6	1		507.2.j.c		2
91.bc	even	12	4		507.2.e.e		4
273.g	even	2	1		117.2.b.a		2
273.o	odd	4	2		1521.2.a.l		2
364.h	even	2	1		624.2.c.e		2
364.p	odd	4	2		8112.2.a.bv		2
455.h	odd	2	1		975.2.b.d		2
455.s	even	4	2		975.2.h.f		4
728.b	even	2	1		2496.2.c.d		2
728.l	odd	2	1		2496.2.c.k		2
1092.d	odd	2	1		1872.2.c.e		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
39.2.b.a	✓	2	7.b	odd	2	1
39.2.b.a	✓	2	91.b	odd	2	1
117.2.b.a		2	21.c	even	2	1
117.2.b.a		2	273.g	even	2	1
507.2.a.f		2	91.i	even	4	2
507.2.e.e		4	91.bc	even	12	4
507.2.j.a		2	91.n	odd	6	1
507.2.j.a		2	91.t	odd	6	1
507.2.j.c		2	91.n	odd	6	1
507.2.j.c		2	91.t	odd	6	1
624.2.c.e		2	28.d	even	2	1
624.2.c.e		2	364.h	even	2	1
975.2.b.d		2	35.c	odd	2	1
975.2.b.d		2	455.h	odd	2	1
975.2.h.f		4	35.f	even	4	2
975.2.h.f		4	455.s	even	4	2
1521.2.a.l		2	273.o	odd	4	2
1872.2.c.e		2	84.h	odd	2	1
1872.2.c.e		2	1092.d	odd	2	1
1911.2.c.d		2	1.a	even	1	1	trivial
1911.2.c.d		2	13.b	even	2	1	inner
2496.2.c.d		2	56.e	even	2	1
2496.2.c.d		2	728.b	even	2	1
2496.2.c.k		2	56.h	odd	2	1
2496.2.c.k		2	728.l	odd	2	1
8112.2.a.bv		2	364.p	odd	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1911, [\chi])\):

\( T_{2}^{2} + 3 \)

\( T_{5} \)

\( T_{17} - 6 \)

Hecke characteristic polynomials

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