Newform orbit 2205.4.a.bv

• Label: 2205.4.a.bv
• Level: $2205$
• Weight: $4$
• Character orbit: 2205.a
• Self dual: yes
• Analytic conductor: $130.099$
• Analytic rank: $0$
• Dimension: $5$
• 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:	\(5\)
Coefficient field:	\(\mathbb{Q}[x]/(x^{5} - \cdots)\)
Defining polynomial:	\( x^{5} - x^{4} - 30x^{3} + 2x^{2} + 164x + 84 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index:	\( 2\cdot 7 \)
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 a basis \(1,\beta_1,\beta_2,\beta_3,\beta_4\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	\( q + \beta_1 q^{2} + (\beta_{2} + \beta_1 + 4) q^{4} - 5 q^{5} + (\beta_{3} + \beta_{2} + 4 \beta_1 + 13) q^{8}+O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 21 q^{4} - 25 q^{5} + 69 q^{8}+O(q^{10}) \)

Basis of coefficient ring in terms of a root \(\nu\) of \( x^{5} - x^{4} - 30x^{3} + 2x^{2} + 164x + 84 \) :

\(\beta_{1}\)	\(=\)	\( \nu \)
\(\beta_{2}\)	\(=\)	\( \nu^{2} - \nu - 12 \)
\(\beta_{3}\)	\(=\)	\( \nu^{3} - \nu^{2} - 19\nu - 1 \)
\(\beta_{4}\)	\(=\)	\( ( \nu^{4} - 3\nu^{3} - 24\nu^{2} + 44\nu + 84 ) / 2 \)

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

−4.27800
−2.37290
−0.544516
2.83495
5.36047

−4.27800

0

10.3013

−5.00000

0

0

−9.84488

0

21.3900

1.2

−2.37290

0

−2.36934

−5.00000

0

0

24.6054

0

11.8645

1.3

−0.544516

0

−7.70350

−5.00000

0

0

8.55081

0

2.72258

1.4

2.83495

0

0.0369369

−5.00000

0

0

−22.5749

0

−14.1747

1.5

5.36047

0

20.7346

−5.00000

0

0

68.2635

0

−26.8023

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.bv		5
3.b	odd	2	1		735.4.a.x		5
7.b	odd	2	1		2205.4.a.bw		5
7.d	odd	6	2		315.4.j.f		10
21.c	even	2	1		735.4.a.y		5
21.g	even	6	2		105.4.i.e	✓	10

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
105.4.i.e	✓	10	21.g	even	6	2
315.4.j.f		10	7.d	odd	6	2
735.4.a.x		5	3.b	odd	2	1
735.4.a.y		5	21.c	even	2	1
2205.4.a.bv		5	1.a	even	1	1	trivial
2205.4.a.bw		5	7.b	odd	2	1

Hecke kernels

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

\( T_{2}^{5} - T_{2}^{4} - 30T_{2}^{3} + 2T_{2}^{2} + 164T_{2} + 84 \)

\( T_{11}^{5} - 33T_{11}^{4} - 4896T_{11}^{3} + 131808T_{11}^{2} + 3902092T_{11} + 1409268 \)

\( T_{13}^{5} - 23T_{13}^{4} - 5870T_{13}^{3} + 134666T_{13}^{2} + 4614873T_{13} + 25478281 \)

\( T_{17}^{5} + 136T_{17}^{4} - 23696T_{17}^{3} - 3244176T_{17}^{2} + 135075692T_{17} + 18600240000 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	T^5 - T^4 - 30*T^3 + 2*T^2 + 164*T + 84
$3$	\( T^{5} \)
$5$	\( (T + 5)^{5} \)
$7$	\( T^{5} \)
$11$	T^5 - 33*T^4 - 4896*T^3 + 131808*T^2 + 3902092*T + 1409268