Newform orbit 864.2.v.b

• Label: 864.2.v.b
• Level: $864$
• Weight: $2$
• Character orbit: 864.v
• Analytic conductor: $6.899$
• Analytic rank: $0$
• Dimension: $128$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.v (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(6.89907473464\)
Analytic rank:	\(0\)
Dimension:	\(128\)
Relative dimension:	\(32\) over \(\Q(\zeta_{8})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 128 q + O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
109.1	−1.41128	−	0.0910249i		0		1.98343	+	0.256923i	2.84116	−	1.17684i		0		−0.237847	+	0.237847i	−2.77579	−	0.543133i		0		−4.11679	+	1.40224i
109.2	−1.39831	+	0.211463i		0		1.91057	−	0.591382i	−1.77214	+	0.734044i		0		−0.0355868	+	0.0355868i	−2.54652	+	1.23095i		0		2.32278	−	1.40116i
109.3	−1.33723	−	0.460244i		0		1.57635	+	1.23090i	−2.37116	+	0.982165i		0		2.29537	−	2.29537i	−1.54142	−	2.37150i		0		3.62281	−	0.222067i
109.4	−1.23997	+	0.680049i		0		1.07507	−	1.68649i	1.02237	−	0.423478i		0		0.485592	−	0.485592i	−0.186159	+	2.82229i		0		−0.979722	+	1.22036i
109.5	−1.19327	+	0.759019i		0		0.847781	−	1.81143i	2.08348	−	0.863006i		0		−2.85037	+	2.85037i	0.363276	+	2.80500i		0		−1.83111	+	2.61120i
109.6	−1.14607	−	0.828563i		0		0.626968	+	1.89919i	−2.89399	+	1.19873i		0		−3.03933	+	3.03933i	0.855044	−	2.69609i		0		4.30995	+	1.02402i
109.7	−1.12159	−	0.861417i		0		0.515922	+	1.93231i	1.04543	−	0.433032i		0		2.00753	−	2.00753i	1.08587	−	2.61168i		0		−1.54557	−	0.414869i
109.8	−1.11341	+	0.871966i		0		0.479352	−	1.94171i	−2.70909	+	1.12214i		0		0.103960	−	0.103960i	1.15939	+	2.57989i		0		2.03785	−	3.61163i
109.9	−0.933793	−	1.06209i		0		−0.256062	+	1.98354i	1.30670	−	0.541253i		0		−1.80429	+	1.80429i	2.34580	−	1.58026i		0		−1.79505	−	0.882413i
109.10	−0.877362	+	1.10916i		0		−0.460473	−	1.94627i	3.16129	−	1.30945i		0		3.16733	−	3.16733i	2.56273	+	1.19684i		0		−1.32120	+	4.65523i
109.11	−0.679990	+	1.24001i		0		−1.07523	−	1.68638i	−3.54476	+	1.46829i		0		1.60611	−	1.60611i	2.82227	−	0.186565i		0		0.589716	−	5.39394i
109.12	−0.479175	+	1.33056i		0		−1.54078	−	1.27514i	−0.855212	+	0.354240i		0		−3.04155	+	3.04155i	2.43496	−	1.43909i		0		−0.0615424	−	1.30765i
109.13	−0.463875	−	1.33597i		0		−1.56964	+	1.23945i	−0.137547	+	0.0569738i		0		0.385875	−	0.385875i	2.38398	+	1.52205i		0		0.139920	+	0.157330i
109.14	−0.322202	−	1.37702i		0		−1.79237	+	0.887359i	1.57161	−	0.650984i		0		3.07534	−	3.07534i	1.79942	+	2.18222i		0		−1.40280	−	1.95440i
109.15	−0.274404	−	1.38734i		0		−1.84940	+	0.761382i	−3.91016	+	1.61964i		0		−0.876571	+	0.876571i	1.56378	+	2.35682i		0		3.31995	+	4.98027i
109.16	−0.239074	+	1.39386i		0		−1.88569	−	0.666470i	0.369546	−	0.153071i		0		−1.24156	+	1.24156i	1.37978	−	2.46905i		0		0.125011	+	0.551690i
109.17	0.239074	−	1.39386i		0		−1.88569	−	0.666470i	−0.369546	+	0.153071i		0		−1.24156	+	1.24156i	−1.37978	+	2.46905i		0		0.125011	+	0.551690i
109.18	0.274404	+	1.38734i		0		−1.84940	+	0.761382i	3.91016	−	1.61964i		0		−0.876571	+	0.876571i	−1.56378	−	2.35682i		0		3.31995	+	4.98027i
109.19	0.322202	+	1.37702i		0		−1.79237	+	0.887359i	−1.57161	+	0.650984i		0		3.07534	−	3.07534i	−1.79942	−	2.18222i		0		−1.40280	−	1.95440i
109.20	0.463875	+	1.33597i		0		−1.56964	+	1.23945i	0.137547	−	0.0569738i		0		0.385875	−	0.385875i	−2.38398	−	1.52205i		0		0.139920	+	0.157330i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner
32.g	even	8	1	inner
96.p	odd	8	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	864.2.v.b	✓	128
3.b	odd	2	1	inner	864.2.v.b	✓	128
32.g	even	8	1	inner	864.2.v.b	✓	128
96.p	odd	8	1	inner	864.2.v.b	✓	128

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
864.2.v.b	✓	128	1.a	even	1	1	trivial
864.2.v.b	✓	128	3.b	odd	2	1	inner
864.2.v.b	✓	128	32.g	even	8	1	inner
864.2.v.b	✓	128	96.p	odd	8	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(30\!\cdots\!68\)\( T_{5}^{106} + \)\(40\!\cdots\!80\)\( T_{5}^{104} - \)\(84\!\cdots\!36\)\( T_{5}^{102} + \)\(91\!\cdots\!88\)\( T_{5}^{100} - \)\(21\!\cdots\!68\)\( T_{5}^{98} + \)\(50\!\cdots\!04\)\( T_{5}^{96} - \)\(10\!\cdots\!44\)\( T_{5}^{94} + \)\(10\!\cdots\!48\)\( T_{5}^{92} + \)\(30\!\cdots\!28\)\( T_{5}^{90} + \)\(31\!\cdots\!12\)\( T_{5}^{88} - \)\(53\!\cdots\!80\)\( T_{5}^{86} + \)\(44\!\cdots\!44\)\( T_{5}^{84} + \)\(31\!\cdots\!68\)\( T_{5}^{82} + \)\(97\!\cdots\!64\)\( T_{5}^{80} - \)\(12\!\cdots\!16\)\( T_{5}^{78} + \)\(76\!\cdots\!28\)\( T_{5}^{76} - \)\(67\!\cdots\!52\)\( T_{5}^{74} + \)\(14\!\cdots\!52\)\( T_{5}^{72} - \)\(17\!\cdots\!96\)\( T_{5}^{70} + \)\(98\!\cdots\!36\)\( T_{5}^{68} - \)\(29\!\cdots\!20\)\( T_{5}^{66} + \)\(10\!\cdots\!72\)\( T_{5}^{64} - \)\(15\!\cdots\!80\)\( T_{5}^{62} + \)\(13\!\cdots\!92\)\( T_{5}^{60} - \)\(19\!\cdots\!32\)\( T_{5}^{58} + \)\(28\!\cdots\!40\)\( T_{5}^{56} - \)\(60\!\cdots\!32\)\( T_{5}^{54} + \)\(74\!\cdots\!24\)\( T_{5}^{52} - \)\(26\!\cdots\!88\)\( T_{5}^{50} + \)\(24\!\cdots\!28\)\( T_{5}^{48} - \)\(61\!\cdots\!12\)\( T_{5}^{46} + \)\(84\!\cdots\!72\)\( T_{5}^{44} - \)\(66\!\cdots\!08\)\( T_{5}^{42} + \)\(24\!\cdots\!44\)\( T_{5}^{40} - \)\(60\!\cdots\!88\)\( T_{5}^{38} + \)\(83\!\cdots\!08\)\( T_{5}^{36} - \)\(48\!\cdots\!08\)\( T_{5}^{34} + \)\(31\!\cdots\!60\)\( T_{5}^{32} - \)\(57\!\cdots\!48\)\( T_{5}^{30} + \)\(90\!\cdots\!36\)\( T_{5}^{28} - \)\(47\!\cdots\!24\)\( T_{5}^{26} + \)\(72\!\cdots\!56\)\( T_{5}^{24} + \)\(69\!\cdots\!52\)\( T_{5}^{22} + \)\(23\!\cdots\!80\)\( T_{5}^{20} + \)\(11\!\cdots\!60\)\( T_{5}^{18} + \)\(13\!\cdots\!48\)\( T_{5}^{16} + \)\(57\!\cdots\!12\)\( T_{5}^{14} + \)\(12\!\cdots\!28\)\( T_{5}^{12} + \)\(11\!\cdots\!96\)\( T_{5}^{10} + \)\(59\!\cdots\!12\)\( T_{5}^{8} + \)\(10\!\cdots\!84\)\( T_{5}^{6} + \)\(28\!\cdots\!00\)\( T_{5}^{4} - \)\(12\!\cdots\!40\)\( T_{5}^{2} + \)\(28\!\cdots\!96\)\( \)">\(T_{5}^{128} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(864, [\chi])\).