Newform orbit 950.2.n.a

• Label: 950.2.n.a
• Level: $950$
• Weight: $2$
• Character orbit: 950.n
• Analytic conductor: $7.586$
• Analytic rank: $0$
• Dimension: $88$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.n (of order \(10\), degree \(4\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.58578819202\)
Analytic rank:	\(0\)
Dimension:	\(88\)
Relative dimension:	\(22\) over \(\Q(\zeta_{10})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 88q + 22q^{4} + 10q^{5} + 2q^{6} + 24q^{9} + O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
39.1	−0.587785	−	0.809017i	−2.56558	−	0.833609i	−0.309017	+	0.951057i	0.0605232	+	2.23525i	0.833609	+	2.56558i		−	3.84106i	0.951057	−	0.309017i	3.46027	+	2.51403i	1.77278	−	1.36281i
39.2	−0.587785	−	0.809017i	−2.20724	−	0.717177i	−0.309017	+	0.951057i	2.23210	−	0.133199i	0.717177	+	2.20724i		−	2.34643i	0.951057	−	0.309017i	1.93053	+	1.40261i	−1.41975	−	1.72751i
39.3	−0.587785	−	0.809017i	−2.20015	−	0.714873i	−0.309017	+	0.951057i	−2.17200	−	0.531443i	0.714873	+	2.20015i			2.86995i	0.951057	−	0.309017i	1.90257	+	1.38230i	0.846721	+	2.06956i
39.4	−0.587785	−	0.809017i	−1.06179	−	0.344997i	−0.309017	+	0.951057i	−0.518181	−	2.17520i	0.344997	+	1.06179i			0.133310i	0.951057	−	0.309017i	−1.41867	−	1.03073i	−1.45519	+	1.69777i
39.5	−0.587785	−	0.809017i	−0.812784	−	0.264090i	−0.309017	+	0.951057i	0.775807	+	2.09717i	0.264090	+	0.812784i			3.74573i	0.951057	−	0.309017i	−1.83618	−	1.33406i	1.24064	−	1.86033i
39.6	−0.587785	−	0.809017i	−0.273661	−	0.0889179i	−0.309017	+	0.951057i	−1.60391	+	1.55803i	0.0889179	+	0.273661i		−	0.224849i	0.951057	−	0.309017i	−2.36007	−	1.71469i	2.20323	+	0.381801i
39.7	−0.587785	−	0.809017i	0.236785	+	0.0769362i	−0.309017	+	0.951057i	−1.89595	−	1.18549i	−0.0769362	−	0.236785i		−	4.79883i	0.951057	−	0.309017i	−2.37690	−	1.72692i	0.155332	+	2.23067i
39.8	−0.587785	−	0.809017i	1.25142	+	0.406611i	−0.309017	+	0.951057i	1.47560	−	1.68006i	−0.406611	−	1.25142i			2.56926i	0.951057	−	0.309017i	−1.02633	−	0.745671i	−2.22653	−	0.206269i
39.9	−0.587785	−	0.809017i	1.63623	+	0.531642i	−0.309017	+	0.951057i	1.99525	−	1.00944i	−0.531642	−	1.63623i		−	3.69408i	0.951057	−	0.309017i	−0.0324603	−	0.0235838i	−1.98943	−	1.02086i
39.10	−0.587785	−	0.809017i	2.87975	+	0.935689i	−0.309017	+	0.951057i	0.587147	+	2.15760i	−0.935689	−	2.87975i			1.61619i	0.951057	−	0.309017i	4.99042	+	3.62575i	1.40042	−	1.74322i
39.11	−0.587785	−	0.809017i	2.95005	+	0.958531i	−0.309017	+	0.951057i	1.23590	−	1.86348i	−0.958531	−	2.95005i		−	2.65378i	0.951057	−	0.309017i	5.35699	+	3.89208i	−2.23403	+	0.0954627i
39.12	0.587785	+	0.809017i	−3.09795	−	1.00658i	−0.309017	+	0.951057i	−0.367092	+	2.20573i	−1.00658	−	3.09795i			4.43412i	−0.951057	+	0.309017i	6.15701	+	4.47333i	−2.00024	+	0.999512i
39.13	0.587785	+	0.809017i	−1.88808	−	0.613474i	−0.309017	+	0.951057i	2.21981	+	0.269141i	−0.613474	−	1.88808i			0.715850i	−0.951057	+	0.309017i	0.761435	+	0.553215i	1.08703	+	1.95406i
39.14	0.587785	+	0.809017i	−1.78167	−	0.578899i	−0.309017	+	0.951057i	0.452104	−	2.18989i	−0.578899	−	1.78167i		−	4.62971i	−0.951057	+	0.309017i	0.412164	+	0.299454i	2.03740	−	0.921423i
39.15	0.587785	+	0.809017i	−1.70705	−	0.554656i	−0.309017	+	0.951057i	−2.20234	+	0.386932i	−0.554656	−	1.70705i		−	2.40506i	−0.951057	+	0.309017i	0.179341	+	0.130299i	−1.60753	−	1.55429i
39.16	0.587785	+	0.809017i	−1.33501	−	0.433772i	−0.309017	+	0.951057i	0.407477	+	2.19863i	−0.433772	−	1.33501i		−	1.42943i	−0.951057	+	0.309017i	−0.832948	−	0.605172i	−1.53922	+	1.62198i
39.17	0.587785	+	0.809017i	−0.284260	−	0.0923618i	−0.309017	+	0.951057i	0.810167	−	2.08414i	−0.0923618	−	0.284260i			5.14607i	−0.951057	+	0.309017i	−2.35478	−	1.71085i	2.16231	−	0.569586i
39.18	0.587785	+	0.809017i	0.285827	+	0.0928709i	−0.309017	+	0.951057i	2.23251	−	0.126065i	0.0928709	+	0.285827i		−	0.304227i	−0.951057	+	0.309017i	−2.35398	−	1.71027i	1.41423	+	1.73204i
39.19	0.587785	+	0.809017i	0.718550	+	0.233471i	−0.309017	+	0.951057i	−1.61612	−	1.54537i	0.233471	+	0.718550i		−	0.567373i	−0.951057	+	0.309017i	−1.96525	−	1.42783i	0.300299	−	2.21581i
39.20	0.587785	+	0.809017i	1.55730	+	0.505997i	−0.309017	+	0.951057i	−0.854432	+	2.06638i	0.505997	+	1.55730i			0.994490i	−0.951057	+	0.309017i	−0.257907	−	0.187380i	−2.17396	+	0.523340i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
25.e	even	10	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	950.2.n.a	✓	88
25.e	even	10	1	inner	950.2.n.a	✓	88

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
950.2.n.a	✓	88	1.a	even	1	1	trivial
950.2.n.a	✓	88	25.e	even	10	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(20\!\cdots\!11\)\( T_{3}^{66} + \)\(37\!\cdots\!40\)\( T_{3}^{65} + \)\(13\!\cdots\!67\)\( T_{3}^{64} - \)\(22\!\cdots\!10\)\( T_{3}^{63} - \)\(80\!\cdots\!37\)\( T_{3}^{62} + \)\(12\!\cdots\!10\)\( T_{3}^{61} + \)\(44\!\cdots\!81\)\( T_{3}^{60} - \)\(58\!\cdots\!70\)\( T_{3}^{59} - \)\(22\!\cdots\!01\)\( T_{3}^{58} + \)\(25\!\cdots\!20\)\( T_{3}^{57} + \)\(10\!\cdots\!42\)\( T_{3}^{56} - \)\(94\!\cdots\!50\)\( T_{3}^{55} - \)\(46\!\cdots\!84\)\( T_{3}^{54} + \)\(30\!\cdots\!40\)\( T_{3}^{53} + \)\(18\!\cdots\!89\)\( T_{3}^{52} - \)\(73\!\cdots\!70\)\( T_{3}^{51} - \)\(66\!\cdots\!64\)\( T_{3}^{50} + \)\(11\!\cdots\!20\)\( T_{3}^{49} + \)\(21\!\cdots\!42\)\( T_{3}^{48} + \)\(16\!\cdots\!50\)\( T_{3}^{47} - \)\(63\!\cdots\!64\)\( T_{3}^{46} - \)\(21\!\cdots\!00\)\( T_{3}^{45} + \)\(16\!\cdots\!97\)\( T_{3}^{44} + \)\(10\!\cdots\!30\)\( T_{3}^{43} - \)\(35\!\cdots\!59\)\( T_{3}^{42} - \)\(32\!\cdots\!50\)\( T_{3}^{41} + \)\(68\!\cdots\!82\)\( T_{3}^{40} + \)\(85\!\cdots\!30\)\( T_{3}^{39} - \)\(11\!\cdots\!99\)\( T_{3}^{38} - \)\(19\!\cdots\!30\)\( T_{3}^{37} + \)\(13\!\cdots\!59\)\( T_{3}^{36} + \)\(36\!\cdots\!50\)\( T_{3}^{35} - \)\(94\!\cdots\!84\)\( T_{3}^{34} - \)\(53\!\cdots\!00\)\( T_{3}^{33} + \)\(38\!\cdots\!42\)\( T_{3}^{32} + \)\(74\!\cdots\!80\)\( T_{3}^{31} + \)\(13\!\cdots\!39\)\( T_{3}^{30} - \)\(88\!\cdots\!50\)\( T_{3}^{29} - \)\(38\!\cdots\!84\)\( T_{3}^{28} + \)\(87\!\cdots\!10\)\( T_{3}^{27} + \)\(63\!\cdots\!58\)\( T_{3}^{26} - \)\(56\!\cdots\!30\)\( T_{3}^{25} - \)\(47\!\cdots\!33\)\( T_{3}^{24} + \)\(67\!\cdots\!30\)\( T_{3}^{23} + \)\(80\!\cdots\!99\)\( T_{3}^{22} - \)\(10\!\cdots\!90\)\( T_{3}^{21} - \)\(43\!\cdots\!18\)\( T_{3}^{20} + \)\(72\!\cdots\!90\)\( T_{3}^{19} + \)\(31\!\cdots\!16\)\( T_{3}^{18} + \)\(17\!\cdots\!20\)\( T_{3}^{17} - \)\(18\!\cdots\!19\)\( T_{3}^{16} - \)\(60\!\cdots\!70\)\( T_{3}^{15} + \)\(75\!\cdots\!54\)\( T_{3}^{14} + \)\(63\!\cdots\!60\)\( T_{3}^{13} + \)\(75\!\cdots\!68\)\( T_{3}^{12} - \)\(90\!\cdots\!40\)\( T_{3}^{11} - \)\(23\!\cdots\!72\)\( T_{3}^{10} + \)\(10\!\cdots\!60\)\( T_{3}^{9} + \)\(36\!\cdots\!68\)\( T_{3}^{8} - \)\(13\!\cdots\!20\)\( T_{3}^{7} - \)\(52\!\cdots\!68\)\( T_{3}^{6} + \)\(14\!\cdots\!60\)\( T_{3}^{5} + \)\(59\!\cdots\!12\)\( T_{3}^{4} - \)\(81\!\cdots\!20\)\( T_{3}^{3} - \)\(35\!\cdots\!00\)\( T_{3}^{2} + \)\(20\!\cdots\!80\)\( T_{3} + \)\(94\!\cdots\!16\)\( \)">\(T_{3}^{88} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(950, [\chi])\).