Newform orbit 63.6.p.b

• Label: 63.6.p.b
• Level: $63$
• Weight: $6$
• Character orbit: 63.p
• Analytic conductor: $10.104$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $4$

Newspace parameters

Level:	$N$	$=$	$63 = 3^{2} \cdot 7$
Weight:	$k$	$=$	$6$
Character orbit:	$[\chi]$	$=$	63.p (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

The algebraic $q$-expansion of this newform has not been computed, but we have computed the trace expansion.

$\operatorname{Tr}(f)(q) =$ 24 * q + 304 * q^4 - 436 * q^7 + 1992 * q^10 - 3644 * q^16 + 3804 * q^19 - 5648 * q^22 - 18852 * q^25 - 39172 * q^28 + 38652 * q^31 + 20548 * q^37 + 132060 * q^40 + 2200 * q^43 - 25712 * q^46 - 125676 * q^49 - 2940 * q^52 + 154300 * q^58 + 48504 * q^61 - 327880 * q^64 + 156324 * q^67 - 9468 * q^70 - 703236 * q^73 + 165756 * q^79 + 1081020 * q^82 - 284448 * q^85 + 582308 * q^88 - 19812 * q^91 - 1481724 * q^94

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	$a_{2}$			$a_{3}$			$a_{4}$			$a_{5}$			$a_{6}$			$a_{7}$			$a_{8}$			$a_{9}$			$a_{10}$
17.1	−9.49029	+	5.47922i		0		44.0437	−	76.2859i	−41.3063	−	71.5446i		0		−18.0992	−	128.372i			614.630i		0		784.017	+	452.652i
17.2	−8.14327	+	4.70152i		0		28.2086	−	48.8587i	33.1882	+	57.4837i		0		−116.271	−	57.3420i			229.595i		0		−540.521	−	312.070i
17.3	−6.73742	+	3.88985i		0		14.2619	−	24.7023i	−46.8267	−	81.1063i		0		58.7189	+	115.582i		−	27.0441i		0		630.983	+	364.298i
17.4	−5.81384	+	3.35662i		0		6.53381	−	11.3169i	43.0174	+	74.5084i		0		95.4202	−	87.7609i		−	127.098i		0		−500.193	−	288.786i
17.5	−4.55322	+	2.62880i		0		−2.17881	+	3.77381i	−11.2537	−	19.4920i		0		−61.1173	+	114.331i		−	191.154i		0		102.481	+	59.1675i
17.6	−1.30242	+	0.751952i		0		−14.8691	+	25.7541i	−8.15150	−	14.1188i		0		−67.6518	−	110.590i		−	92.8484i		0		21.2333	+	12.2591i
17.7	1.30242	−	0.751952i		0		−14.8691	+	25.7541i	8.15150	+	14.1188i		0		−67.6518	−	110.590i			92.8484i		0		21.2333	+	12.2591i
17.8	4.55322	−	2.62880i		0		−2.17881	+	3.77381i	11.2537	+	19.4920i		0		−61.1173	+	114.331i			191.154i		0		102.481	+	59.1675i
17.9	5.81384	−	3.35662i		0		6.53381	−	11.3169i	−43.0174	−	74.5084i		0		95.4202	−	87.7609i			127.098i		0		−500.193	−	288.786i
17.10	6.73742	−	3.88985i		0		14.2619	−	24.7023i	46.8267	+	81.1063i		0		58.7189	+	115.582i			27.0441i		0		630.983	+	364.298i
17.11	8.14327	−	4.70152i		0		28.2086	−	48.8587i	−33.1882	−	57.4837i		0		−116.271	−	57.3420i		−	229.595i		0		−540.521	−	312.070i
17.12	9.49029	−	5.47922i		0		44.0437	−	76.2859i	41.3063	+	71.5446i		0		−18.0992	−	128.372i		−	614.630i		0		784.017	+	452.652i
26.1	−9.49029	−	5.47922i		0		44.0437	+	76.2859i	−41.3063	+	71.5446i		0		−18.0992	+	128.372i		−	614.630i		0		784.017	−	452.652i
26.2	−8.14327	−	4.70152i		0		28.2086	+	48.8587i	33.1882	−	57.4837i		0		−116.271	+	57.3420i		−	229.595i		0		−540.521	+	312.070i
26.3	−6.73742	−	3.88985i		0		14.2619	+	24.7023i	−46.8267	+	81.1063i		0		58.7189	−	115.582i			27.0441i		0		630.983	−	364.298i
26.4	−5.81384	−	3.35662i		0		6.53381	+	11.3169i	43.0174	−	74.5084i		0		95.4202	+	87.7609i			127.098i		0		−500.193	+	288.786i
26.5	−4.55322	−	2.62880i		0		−2.17881	−	3.77381i	−11.2537	+	19.4920i		0		−61.1173	−	114.331i			191.154i		0		102.481	−	59.1675i
26.6	−1.30242	−	0.751952i		0		−14.8691	−	25.7541i	−8.15150	+	14.1188i		0		−67.6518	+	110.590i			92.8484i		0		21.2333	−	12.2591i
26.7	1.30242	+	0.751952i		0		−14.8691	−	25.7541i	8.15150	−	14.1188i		0		−67.6518	+	110.590i		−	92.8484i		0		21.2333	−	12.2591i
26.8	4.55322	+	2.62880i		0		−2.17881	−	3.77381i	11.2537	−	19.4920i		0		−61.1173	−	114.331i		−	191.154i		0		102.481	−	59.1675i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
7.d	odd	6	1	inner
21.g	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	63.6.p.b	✓	24
3.b	odd	2	1	inner	63.6.p.b	✓	24
7.c	even	3	1		441.6.c.b		24
7.d	odd	6	1	inner	63.6.p.b	✓	24
7.d	odd	6	1		441.6.c.b		24
21.g	even	6	1	inner	63.6.p.b	✓	24
21.g	even	6	1		441.6.c.b		24
21.h	odd	6	1		441.6.c.b		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
63.6.p.b	✓	24	1.a	even	1	1	trivial
63.6.p.b	✓	24	3.b	odd	2	1	inner
63.6.p.b	✓	24	7.d	odd	6	1	inner
63.6.p.b	✓	24	21.g	even	6	1	inner
441.6.c.b		24	7.c	even	3	1
441.6.c.b		24	7.d	odd	6	1
441.6.c.b		24	21.g	even	6	1
441.6.c.b		24	21.h	odd	6	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^24 - 344*T2^22 + 73519*T2^20 - 9883100*T2^18 + 975017677*T2^16 - 68764950302*T2^14 + 3663641491264*T2^12 - 139603771636472*T2^10 + 3906108154885840*T2^8 - 69376302085328640*T2^6 + 796304645351919360*T2^4 - 1759475339393753088*T2^2 + 3278535641010671616