Newform orbit 2205.4.a.v

• Label: 2205.4.a.v
• Level: $2205$
• Weight: $4$
• Character orbit: 2205.a
• Self dual: yes
• Analytic conductor: $130.099$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2205.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(130.099211563\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{41}) \)
Defining polynomial:	\( x^{2} - x - 10 \)
Coefficient ring:	\(\Z[a_1, a_2]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 105)
Fricke sign:	\(1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{41})\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	\( q + ( - \beta - 1) q^{2} + (3 \beta + 3) q^{4} - 5 q^{5} + ( - \beta - 25) q^{8}+O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} + 9 q^{4} - 10 q^{5} - 51 q^{8}+O(q^{10}) \)

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

3.70156
−2.70156

−4.70156

0

14.1047

−5.00000

0

0

−28.7016

0

23.5078

1.2

1.70156

0

−5.10469

−5.00000

0

0

−22.2984

0

−8.50781

Atkin-Lehner signs

\( p \)	Sign
\(3\)	\(-1\)
\(5\)	\(1\)
\(7\)	\(-1\)

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	2205.4.a.v		2
3.b	odd	2	1		735.4.a.q		2
7.b	odd	2	1		315.4.a.g		2
21.c	even	2	1		105.4.a.g	✓	2
35.c	odd	2	1		1575.4.a.y		2
84.h	odd	2	1		1680.4.a.y		2
105.g	even	2	1		525.4.a.i		2
105.k	odd	4	2		525.4.d.j		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
105.4.a.g	✓	2	21.c	even	2	1
315.4.a.g		2	7.b	odd	2	1
525.4.a.i		2	105.g	even	2	1
525.4.d.j		4	105.k	odd	4	2
735.4.a.q		2	3.b	odd	2	1
1575.4.a.y		2	35.c	odd	2	1
1680.4.a.y		2	84.h	odd	2	1
2205.4.a.v		2	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(2205))\):

\( T_{2}^{2} + 3T_{2} - 8 \)

\( T_{11}^{2} + 62T_{11} + 920 \)

\( T_{13}^{2} - 6T_{13} - 1016 \)

\( T_{17}^{2} - 40T_{17} - 1076 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} + 3T - 8 \)
$3$	\( T^{2} \)
$5$	\( (T + 5)^{2} \)
$7$	\( T^{2} \)
$11$	\( T^{2} + 62T + 920 \)