Newform orbit 1089.4.a.v

• Label: 1089.4.a.v
• Level: $1089$
• Weight: $4$
• Character orbit: 1089.a
• Self dual: yes
• Analytic conductor: $64.253$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1089.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(64.2530799963\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{3}) \)
Defining polynomial:	\( x^{2} - 3 \)
Coefficient ring:	\(\Z[a_1, a_2]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 11)
Fricke sign:	\(+1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{3}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	q + (b + 1) * q^2 + (2*b - 4) * q^4 + (-8*b - 1) * q^5 + (4*b - 10) * q^7 + (-10*b - 6) * q^8 + (-9*b - 25) * q^10 + (20*b - 40) * q^13 + (-6*b + 2) * q^14 + (-32*b - 4) * q^16 + (12*b - 62) * q^17 + (-60*b - 36) * q^19 + (30*b - 44) * q^20 + (36*b + 49) * q^23 + (16*b + 68) * q^25 + (-20*b + 20) * q^26 + (-36*b + 64) * q^28 + (-56*b + 72) * q^29 + (28*b - 17) * q^31 + (44*b - 52) * q^32 + (-50*b - 26) * q^34 + (76*b - 86) * q^35 + (-8*b + 27) * q^37 + (-96*b - 216) * q^38 + (58*b + 246) * q^40 + (-4*b + 268) * q^41 + (16*b + 30) * q^43 + (85*b + 157) * q^46 + (120*b + 136) * q^47 + (-80*b - 195) * q^49 + (84*b + 116) * q^50 + (-160*b + 280) * q^52 + (56*b + 246) * q^53 + (76*b - 60) * q^56 + (16*b - 96) * q^58 + (132*b - 317) * q^59 + (-184*b - 420) * q^61 + (11*b + 67) * q^62 + (248*b + 112) * q^64 + (300*b - 440) * q^65 + (-20*b + 377) * q^67 + (-172*b + 320) * q^68 + (-10*b + 142) * q^70 + (-76*b + 339) * q^71 + (468*b + 200) * q^73 + (19*b + 3) * q^74 + (168*b - 216) * q^76 + (-656*b - 158) * q^79 + (64*b + 772) * q^80 + (264*b + 256) * q^82 + (120*b + 234) * q^83 + (484*b - 226) * q^85 + (46*b + 78) * q^86 + (328*b + 921) * q^89 + (-360*b + 640) * q^91 + (-46*b + 20) * q^92 + (256*b + 496) * q^94 + (348*b + 1476) * q^95 + (144*b + 1097) * q^97 + (-275*b - 435) * q^98
\(\operatorname{Tr}(f)(q)\)	\(=\)	2 * q + 2 * q^2 - 8 * q^4 - 2 * q^5 - 20 * q^7 - 12 * q^8 - 50 * q^10 - 80 * q^13 + 4 * q^14 - 8 * q^16 - 124 * q^17 - 72 * q^19 - 88 * q^20 + 98 * q^23 + 136 * q^25 + 40 * q^26 + 128 * q^28 + 144 * q^29 - 34 * q^31 - 104 * q^32 - 52 * q^34 - 172 * q^35 + 54 * q^37 - 432 * q^38 + 492 * q^40 + 536 * q^41 + 60 * q^43 + 314 * q^46 + 272 * q^47 - 390 * q^49 + 232 * q^50 + 560 * q^52 + 492 * q^53 - 120 * q^56 - 192 * q^58 - 634 * q^59 - 840 * q^61 + 134 * q^62 + 224 * q^64 - 880 * q^65 + 754 * q^67 + 640 * q^68 + 284 * q^70 + 678 * q^71 + 400 * q^73 + 6 * q^74 - 432 * q^76 - 316 * q^79 + 1544 * q^80 + 512 * q^82 + 468 * q^83 - 452 * q^85 + 156 * q^86 + 1842 * q^89 + 1280 * q^91 + 40 * q^92 + 992 * q^94 + 2952 * q^95 + 2194 * q^97 - 870 * q^98

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

−1.73205
1.73205

−0.732051

0

−7.46410

12.8564

0

−16.9282

11.3205

0

−9.41154

1.2

2.73205

0

−0.535898

−14.8564

0

−3.07180

−23.3205

0

−40.5885

Atkin-Lehner signs

\( p \)	Sign
\(3\)	\( -1 \)
\(11\)	\( -1 \)

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	1089.4.a.v		2
3.b	odd	2	1		121.4.a.c		2
11.b	odd	2	1		99.4.a.c		2
12.b	even	2	1		1936.4.a.w		2
33.d	even	2	1		11.4.a.a	✓	2
33.f	even	10	4		121.4.c.c		8
33.h	odd	10	4		121.4.c.f		8
44.c	even	2	1		1584.4.a.bc		2
55.d	odd	2	1		2475.4.a.q		2
132.d	odd	2	1		176.4.a.i		2
165.d	even	2	1		275.4.a.b		2
165.l	odd	4	2		275.4.b.c		4
231.h	odd	2	1		539.4.a.e		2
264.m	even	2	1		704.4.a.p		2
264.p	odd	2	1		704.4.a.n		2
429.e	even	2	1		1859.4.a.a		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
11.4.a.a	✓	2	33.d	even	2	1
99.4.a.c		2	11.b	odd	2	1
121.4.a.c		2	3.b	odd	2	1
121.4.c.c		8	33.f	even	10	4
121.4.c.f		8	33.h	odd	10	4
176.4.a.i		2	132.d	odd	2	1
275.4.a.b		2	165.d	even	2	1
275.4.b.c		4	165.l	odd	4	2
539.4.a.e		2	231.h	odd	2	1
704.4.a.n		2	264.p	odd	2	1
704.4.a.p		2	264.m	even	2	1
1089.4.a.v		2	1.a	even	1	1	trivial
1584.4.a.bc		2	44.c	even	2	1
1859.4.a.a		2	429.e	even	2	1
1936.4.a.w		2	12.b	even	2	1
2475.4.a.q		2	55.d	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1089))\):

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

\( T_{5}^{2} + 2T_{5} - 191 \)

\( T_{7}^{2} + 20T_{7} + 52 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} - 2T - 2 \)
$3$	\( T^{2} \)
$5$	\( T^{2} + 2T - 191 \)
$7$	\( T^{2} + 20T + 52 \)
$11$	\( T^{2} \)