Newform orbit 3850.2.a.bj

• Label: 3850.2.a.bj
• Level: $3850$
• Weight: $2$
• Character orbit: 3850.a
• Self dual: yes
• Analytic conductor: $30.742$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 3850 = 2 \cdot 5^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3850.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(30.7424047782\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{5}) \)
Defining polynomial:	\( x^{2} - x - 1 \)
Coefficient ring:	\(\Z[a_1, a_2, a_3]\)
Coefficient ring index:	\( 2 \)
Twist minimal:	no (minimal twist has level 154)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{5}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	\( q - q^{2} + (\beta + 1) q^{3} + q^{4} + ( - \beta - 1) q^{6} - q^{7} - q^{8} + (2 \beta + 3) q^{9}+O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 6 q^{9}+O(q^{10}) \)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1.1

−0.618034
1.61803

−1.00000

−1.23607

1.00000

0

1.23607

−1.00000

−1.00000

−1.47214

0

1.2

−1.00000

3.23607

1.00000

0

−3.23607

−1.00000

−1.00000

7.47214

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1\)
\(11\)	\(-1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	3850.2.a.bj		2
5.b	even	2	1		154.2.a.d	✓	2
5.c	odd	4	2		3850.2.c.q		4
15.d	odd	2	1		1386.2.a.m		2
20.d	odd	2	1		1232.2.a.p		2
35.c	odd	2	1		1078.2.a.w		2
35.i	odd	6	2		1078.2.e.n		4
35.j	even	6	2		1078.2.e.q		4
40.e	odd	2	1		4928.2.a.bk		2
40.f	even	2	1		4928.2.a.bt		2
55.d	odd	2	1		1694.2.a.l		2
105.g	even	2	1		9702.2.a.cu		2
140.c	even	2	1		8624.2.a.bf		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
154.2.a.d	✓	2	5.b	even	2	1
1078.2.a.w		2	35.c	odd	2	1
1078.2.e.n		4	35.i	odd	6	2
1078.2.e.q		4	35.j	even	6	2
1232.2.a.p		2	20.d	odd	2	1
1386.2.a.m		2	15.d	odd	2	1
1694.2.a.l		2	55.d	odd	2	1
3850.2.a.bj		2	1.a	even	1	1	trivial
3850.2.c.q		4	5.c	odd	4	2
4928.2.a.bk		2	40.e	odd	2	1
4928.2.a.bt		2	40.f	even	2	1
8624.2.a.bf		2	140.c	even	2	1
9702.2.a.cu		2	105.g	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(3850))\):

\( T_{3}^{2} - 2T_{3} - 4 \)

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

\( T_{17}^{2} - 4T_{17} - 16 \)

\( T_{19}^{2} + 10T_{19} + 20 \)

Hecke characteristic polynomials

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