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 + (-b - 1) * q^2 + (3*b + 3) * q^4 - 5 * q^5 + (-b - 25) * q^8 + (5*b + 5) * q^10 + (2*b - 32) * q^11 + (10*b - 2) * q^13 + (3*b + 11) * q^16 + (-12*b + 26) * q^17 + (2*b + 60) * q^19 + (-15*b - 15) * q^20 + (28*b + 12) * q^22 + (48*b - 32) * q^23 + 25 * q^25 + (-18*b - 98) * q^26 + (-12*b - 170) * q^29 + (38*b - 52) * q^31 + (-9*b + 159) * q^32 + (-2*b + 94) * q^34 + (80*b - 134) * q^37 + (-64*b - 80) * q^38 + (5*b + 125) * q^40 + (-108*b + 62) * q^41 + (100*b - 248) * q^43 + (-84*b - 36) * q^44 + (-64*b - 448) * q^46 + (140*b - 164) * q^47 + (-25*b - 25) * q^50 + (54*b + 294) * q^52 + (-58*b - 462) * q^53 + (-10*b + 160) * q^55 + (194*b + 290) * q^58 + (76*b + 220) * q^59 + (84*b + 398) * q^61 + (-24*b - 328) * q^62 + (-165*b - 157) * q^64 + (-50*b + 10) * q^65 + (-228*b - 64) * q^67 + (6*b - 282) * q^68 + (-86*b - 112) * q^71 + (38*b - 182) * q^73 + (-26*b - 666) * q^74 + (192*b + 240) * q^76 + (-8*b + 920) * q^79 + (-15*b - 55) * q^80 + (154*b + 1018) * q^82 + (-224*b - 228) * q^83 + (60*b - 130) * q^85 + (48*b - 752) * q^86 + (-20*b + 780) * q^88 + (336*b + 230) * q^89 + (192*b + 1344) * q^92 + (-116*b - 1236) * q^94 + (-10*b - 300) * q^95 + (-278*b + 474) * q^97
\(\operatorname{Tr}(f)(q)\)	\(=\)	2 * q - 3 * q^2 + 9 * q^4 - 10 * q^5 - 51 * q^8 + 15 * q^10 - 62 * q^11 + 6 * q^13 + 25 * q^16 + 40 * q^17 + 122 * q^19 - 45 * q^20 + 52 * q^22 - 16 * q^23 + 50 * q^25 - 214 * q^26 - 352 * q^29 - 66 * q^31 + 309 * q^32 + 186 * q^34 - 188 * q^37 - 224 * q^38 + 255 * q^40 + 16 * q^41 - 396 * q^43 - 156 * q^44 - 960 * q^46 - 188 * q^47 - 75 * q^50 + 642 * q^52 - 982 * q^53 + 310 * q^55 + 774 * q^58 + 516 * q^59 + 880 * q^61 - 680 * q^62 - 479 * q^64 - 30 * q^65 - 356 * q^67 - 558 * q^68 - 310 * q^71 - 326 * q^73 - 1358 * q^74 + 672 * q^76 + 1832 * q^79 - 125 * q^80 + 2190 * q^82 - 680 * q^83 - 200 * q^85 - 1456 * q^86 + 1540 * q^88 + 796 * q^89 + 2880 * q^92 - 2588 * q^94 - 610 * q^95 + 670 * q^97

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

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