Newform orbit 1890.2.i.b

• Label: 1890.2.i.b
• Level: $1890$
• Weight: $2$
• Character orbit: 1890.i
• Analytic conductor: $15.092$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1890 = 2 \cdot 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1890.i (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(15.0917259820\)
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:	\( 1 \)
Twist minimal:	no (minimal twist has level 630)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a primitive root of unity \(\zeta_{6}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	\( q - q^{2} + q^{4} + ( - \zeta_{6} + 1) q^{5} + (\zeta_{6} - 3) q^{7} - q^{8}+O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} + q^{5} - 5 q^{7} - 2 q^{8}+O(q^{10}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1890\mathbb{Z}\right)^\times\).

\(n\)	\(757\)	\(1081\)	\(1541\)
\(\chi(n)\)	\(1\)	\(-\zeta_{6}\)	\(-\zeta_{6}\)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

991.1

0.500000	+	0.866025i
0.500000	−	0.866025i

−1.00000

0

1.00000

0.500000

−

0.866025i

0

−2.50000

+

0.866025i

−1.00000

0

−0.500000

+

0.866025i

1171.1

−1.00000

0

1.00000

0.500000

+

0.866025i

0

−2.50000

−

0.866025i

−1.00000

0

−0.500000

−

0.866025i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
63.h	even	3	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	1890.2.i.b		2
3.b	odd	2	1		630.2.i.c	✓	2
7.c	even	3	1		1890.2.l.c		2
9.c	even	3	1		1890.2.l.c		2
9.d	odd	6	1		630.2.l.a	yes	2
21.h	odd	6	1		630.2.l.a	yes	2
63.h	even	3	1	inner	1890.2.i.b		2
63.j	odd	6	1		630.2.i.c	✓	2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
630.2.i.c	✓	2	3.b	odd	2	1
630.2.i.c	✓	2	63.j	odd	6	1
630.2.l.a	yes	2	9.d	odd	6	1
630.2.l.a	yes	2	21.h	odd	6	1
1890.2.i.b		2	1.a	even	1	1	trivial
1890.2.i.b		2	63.h	even	3	1	inner
1890.2.l.c		2	7.c	even	3	1
1890.2.l.c		2	9.c	even	3	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1890, [\chi])\):

\( T_{11}^{2} + 2T_{11} + 4 \)

\( T_{13}^{2} - 2T_{13} + 4 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( (T + 1)^{2} \)
$3$	\( T^{2} \)
$5$	\( T^{2} - T + 1 \)
$7$	\( T^{2} + 5T + 7 \)
$11$	\( T^{2} + 2T + 4 \)