Newform orbit 144.5.j.a

• Label: 144.5.j.a
• Level: $144$
• Weight: $5$
• Character orbit: 144.j
• Analytic conductor: $14.885$
• Analytic rank: $0$
• Dimension: $64$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	144.j (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.8852746841\)
Analytic rank:	\(0\)
Dimension:	\(64\)
Relative dimension:	\(32\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 64 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
53.1	−3.99599	+	0.179021i		0		15.9359	−	1.43073i	4.26272	−	4.26272i		0			−	67.8116i	−63.4236	+	8.57007i		0		−16.2707	+	17.7969i
53.2	−3.96265	+	0.545372i		0		15.4051	−	4.32223i	−32.9582	+	32.9582i		0				91.2257i	−58.6879	+	25.5290i		0		112.627	−	148.576i
53.3	−3.90380	−	0.871964i		0		14.4794	+	6.80795i	28.2881	−	28.2881i		0			−	32.6158i	−50.5883	−	39.2024i		0		−135.097	+	85.7650i
53.4	−3.79604	+	1.26098i		0		12.8199	−	9.57346i	−26.0633	+	26.0633i		0			−	56.5034i	−36.5928	+	52.5068i		0		66.0721	−	131.803i
53.5	−3.63758	+	1.66373i		0		10.4640	−	12.1039i	7.58976	−	7.58976i		0				20.5358i	−17.9261	+	61.4382i		0		−14.9811	+	40.2357i
53.6	−3.56054	−	1.82278i		0		9.35493	+	12.9802i	−11.2739	+	11.2739i		0				59.2409i	−9.64858	−	63.2685i		0		60.6910	−	19.5913i
53.7	−3.23322	+	2.35506i		0		4.90743	−	15.2288i	21.7739	−	21.7739i		0				40.3118i	19.9979	+	60.7954i		0		−19.1211	+	121.678i
53.8	−3.19584	−	2.40554i		0		4.42674	+	15.3754i	5.53749	−	5.53749i		0				17.8687i	22.8391	−	59.7861i		0		−31.0176	+	4.37625i
53.9	−2.46420	−	3.15083i		0		−3.85546	+	15.5285i	−13.7981	+	13.7981i		0			−	87.5517i	58.4284	−	26.1175i		0		77.4768	+	9.47422i
53.10	−2.07101	+	3.42212i		0		−7.42184	−	14.1745i	−1.95060	+	1.95060i		0				77.3947i	63.8776	+	3.95706i		0		−2.63549	−	10.7149i
53.11	−1.99107	+	3.46924i		0		−8.07128	−	13.8150i	−15.3036	+	15.3036i		0			−	40.6680i	63.9981	−	0.494567i		0		−22.6214	−	83.5624i
53.12	−1.62828	+	3.65359i		0		−10.6974	−	11.8982i	16.0603	−	16.0603i		0			−	58.7683i	60.8893	−	19.7102i		0		32.5270	+	84.8286i
53.13	−1.26022	−	3.79629i		0		−12.8237	+	9.56831i	−18.6477	+	18.6477i		0			−	12.8474i	52.4848	+	36.6244i		0		94.2922	+	47.2919i
53.14	−1.20694	−	3.81357i		0		−13.0866	+	9.20548i	16.8525	−	16.8525i		0				28.3068i	50.9005	+	38.7962i		0		−84.6082	−	43.9283i
53.15	−0.251040	+	3.99211i		0		−15.8740	−	2.00436i	18.2409	−	18.2409i		0				31.9519i	11.9866	−	62.8675i		0		68.2404	+	77.3988i
53.16	−0.135736	−	3.99770i		0		−15.9632	+	1.08526i	32.7994	−	32.7994i		0			−	10.0700i	6.50532	+	63.6685i		0		−135.574	−	126.670i
53.17	0.135736	+	3.99770i		0		−15.9632	+	1.08526i	−32.7994	+	32.7994i		0			−	10.0700i	−6.50532	−	63.6685i		0		−135.574	−	126.670i
53.18	0.251040	−	3.99211i		0		−15.8740	−	2.00436i	−18.2409	+	18.2409i		0				31.9519i	−11.9866	+	62.8675i		0		68.2404	+	77.3988i
53.19	1.20694	+	3.81357i		0		−13.0866	+	9.20548i	−16.8525	+	16.8525i		0				28.3068i	−50.9005	−	38.7962i		0		−84.6082	−	43.9283i
53.20	1.26022	+	3.79629i		0		−12.8237	+	9.56831i	18.6477	−	18.6477i		0			−	12.8474i	−52.4848	−	36.6244i		0		94.2922	+	47.2919i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
16.e	even	4	1	inner
48.i	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	144.5.j.a	✓	64
3.b	odd	2	1	inner	144.5.j.a	✓	64
4.b	odd	2	1		576.5.j.a		64
12.b	even	2	1		576.5.j.a		64
16.e	even	4	1	inner	144.5.j.a	✓	64
16.f	odd	4	1		576.5.j.a		64
48.i	odd	4	1	inner	144.5.j.a	✓	64
48.k	even	4	1		576.5.j.a		64

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
144.5.j.a	✓	64	1.a	even	1	1	trivial
144.5.j.a	✓	64	3.b	odd	2	1	inner
144.5.j.a	✓	64	16.e	even	4	1	inner
144.5.j.a	✓	64	48.i	odd	4	1	inner
576.5.j.a		64	4.b	odd	2	1
576.5.j.a		64	12.b	even	2	1
576.5.j.a		64	16.f	odd	4	1
576.5.j.a		64	48.k	even	4	1

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(144, [\chi])\).