Newform orbit 950.2.n.b

• Label: 950.2.n.b
• Level: $950$
• Weight: $2$
• Character orbit: 950.n
• Analytic conductor: $7.586$
• Analytic rank: $0$
• Dimension: $96$
• 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:	\(96\)
Relative dimension:	\(24\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 96q + 24q^{4} + 8q^{5} - 6q^{6} + 34q^{9} + O(q^{10}) \)

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	−3.22850	−	1.04900i	−0.309017	+	0.951057i	−1.55488	−	1.60697i	1.04900	+	3.22850i		−	3.46343i	0.951057	−	0.309017i	6.89577	+	5.01007i	−0.386131	+	2.20248i
39.2	−0.587785	−	0.809017i	−3.16378	−	1.02797i	−0.309017	+	0.951057i	1.22578	−	1.87015i	1.02797	+	3.16378i			4.52249i	0.951057	−	0.309017i	6.52572	+	4.74121i	−2.23348	+	0.107573i
39.3	−0.587785	−	0.809017i	−2.09906	−	0.682024i	−0.309017	+	0.951057i	−0.131723	+	2.23218i	0.682024	+	2.09906i			4.35569i	0.951057	−	0.309017i	1.51382	+	1.09986i	1.88330	−	1.20548i
39.4	−0.587785	−	0.809017i	−2.06198	−	0.669976i	−0.309017	+	0.951057i	2.16827	+	0.546445i	0.669976	+	2.06198i			0.754312i	0.951057	−	0.309017i	1.37582	+	0.999595i	−0.832394	−	2.07536i
39.5	−0.587785	−	0.809017i	−1.16860	−	0.379700i	−0.309017	+	0.951057i	−2.18761	−	0.463006i	0.379700	+	1.16860i		−	0.0227859i	0.951057	−	0.309017i	−1.20561	−	0.875924i	0.911264	+	2.04196i
39.6	−0.587785	−	0.809017i	−0.408708	−	0.132797i	−0.309017	+	0.951057i	1.37111	−	1.76637i	0.132797	+	0.408708i		−	1.90044i	0.951057	−	0.309017i	−2.27764	−	1.65481i	−2.23494	−	0.0710083i
39.7	−0.587785	−	0.809017i	0.0436702	+	0.0141893i	−0.309017	+	0.951057i	0.459049	+	2.18844i	−0.0141893	−	0.0436702i		−	2.50954i	0.951057	−	0.309017i	−2.42535	−	1.76212i	1.50066	−	1.65771i
39.8	−0.587785	−	0.809017i	0.702911	+	0.228390i	−0.309017	+	0.951057i	−0.520909	−	2.17455i	−0.228390	−	0.702911i			2.52633i	0.951057	−	0.309017i	−1.98513	−	1.44228i	−1.45306	+	1.69959i
39.9	−0.587785	−	0.809017i	1.21854	+	0.395928i	−0.309017	+	0.951057i	1.81457	+	1.30665i	−0.395928	−	1.21854i		−	1.92349i	0.951057	−	0.309017i	−1.09897	−	0.798446i	−0.00947820	−	2.23605i
39.10	−0.587785	−	0.809017i	1.40124	+	0.455290i	−0.309017	+	0.951057i	−1.43867	+	1.71179i	−0.455290	−	1.40124i			2.83916i	0.951057	−	0.309017i	−0.670872	−	0.487417i	2.23050	+	0.157745i
39.11	−0.587785	−	0.809017i	1.83314	+	0.595623i	−0.309017	+	0.951057i	2.21079	−	0.335262i	−0.595623	−	1.83314i			3.44879i	0.951057	−	0.309017i	0.578586	+	0.420367i	−1.57070	−	1.59151i
39.12	−0.587785	−	0.809017i	2.95991	+	0.961734i	−0.309017	+	0.951057i	−2.05251	−	0.887239i	−0.961734	−	2.95991i			0.626185i	0.951057	−	0.309017i	5.40910	+	3.92994i	0.488645	+	2.18202i
39.13	0.587785	+	0.809017i	−3.02842	−	0.983992i	−0.309017	+	0.951057i	1.06990	+	1.96349i	−0.983992	−	3.02842i		−	2.61307i	−0.951057	+	0.309017i	5.77601	+	4.19652i	−0.959627	+	2.01968i
39.14	0.587785	+	0.809017i	−2.52973	−	0.821960i	−0.309017	+	0.951057i	1.13666	−	1.92562i	−0.821960	−	2.52973i			1.29013i	−0.951057	+	0.309017i	3.29688	+	2.39532i	2.22597	−	0.212273i
39.15	0.587785	+	0.809017i	−2.08312	−	0.676848i	−0.309017	+	0.951057i	−1.46374	−	1.69040i	−0.676848	−	2.08312i			1.17098i	−0.951057	+	0.309017i	1.45423	+	1.05656i	0.507200	−	2.17779i
39.16	0.587785	+	0.809017i	−1.43673	−	0.466821i	−0.309017	+	0.951057i	−1.88711	+	1.19951i	−0.466821	−	1.43673i			3.41486i	−0.951057	+	0.309017i	−0.580791	−	0.421969i	−2.07964	−	0.821650i
39.17	0.587785	+	0.809017i	−0.0948098	−	0.0308056i	−0.309017	+	0.951057i	1.43256	−	1.71691i	−0.0308056	−	0.0948098i		−	2.23805i	−0.951057	+	0.309017i	−2.41901	−	1.75751i	2.23105	+	0.149792i
39.18	0.587785	+	0.809017i	−0.0145515	−	0.00472808i	−0.309017	+	0.951057i	1.99515	+	1.00964i	−0.00472808	−	0.0145515i			0.890552i	−0.951057	+	0.309017i	−2.42686	−	1.76322i	0.355906	+	2.20756i
39.19	0.587785	+	0.809017i	0.219108	+	0.0711926i	−0.309017	+	0.951057i	−0.684773	+	2.12863i	0.0711926	+	0.219108i		−	4.22635i	−0.951057	+	0.309017i	−2.38411	−	1.73216i	−2.12460	+	0.697187i
39.20	0.587785	+	0.809017i	1.16397	+	0.378196i	−0.309017	+	0.951057i	−2.21303	+	0.320187i	0.378196	+	1.16397i		−	3.41155i	−0.951057	+	0.309017i	−1.21526	−	0.882938i	−1.55982	−	1.60217i

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.b	✓	96
25.e	even	10	1	inner	950.2.n.b	✓	96

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
950.2.n.b	✓	96	1.a	even	1	1	trivial
950.2.n.b	✓	96	25.e	even	10	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(11\!\cdots\!97\)\( T_{3}^{76} - \)\(43\!\cdots\!20\)\( T_{3}^{75} - \)\(85\!\cdots\!51\)\( T_{3}^{74} + \)\(37\!\cdots\!80\)\( T_{3}^{73} + \)\(56\!\cdots\!23\)\( T_{3}^{72} - \)\(29\!\cdots\!30\)\( T_{3}^{71} - \)\(32\!\cdots\!09\)\( T_{3}^{70} + \)\(21\!\cdots\!70\)\( T_{3}^{69} + \)\(15\!\cdots\!53\)\( T_{3}^{68} - \)\(14\!\cdots\!70\)\( T_{3}^{67} - \)\(58\!\cdots\!97\)\( T_{3}^{66} + \)\(85\!\cdots\!20\)\( T_{3}^{65} + \)\(11\!\cdots\!98\)\( T_{3}^{64} - \)\(47\!\cdots\!50\)\( T_{3}^{63} + \)\(61\!\cdots\!28\)\( T_{3}^{62} + \)\(24\!\cdots\!20\)\( T_{3}^{61} - \)\(91\!\cdots\!27\)\( T_{3}^{60} - \)\(11\!\cdots\!70\)\( T_{3}^{59} + \)\(70\!\cdots\!28\)\( T_{3}^{58} + \)\(48\!\cdots\!60\)\( T_{3}^{57} - \)\(42\!\cdots\!70\)\( T_{3}^{56} - \)\(18\!\cdots\!10\)\( T_{3}^{55} + \)\(21\!\cdots\!32\)\( T_{3}^{54} + \)\(67\!\cdots\!00\)\( T_{3}^{53} - \)\(95\!\cdots\!19\)\( T_{3}^{52} - \)\(21\!\cdots\!90\)\( T_{3}^{51} + \)\(37\!\cdots\!69\)\( T_{3}^{50} + \)\(59\!\cdots\!70\)\( T_{3}^{49} - \)\(13\!\cdots\!54\)\( T_{3}^{48} - \)\(14\!\cdots\!10\)\( T_{3}^{47} + \)\(41\!\cdots\!49\)\( T_{3}^{46} + \)\(29\!\cdots\!70\)\( T_{3}^{45} - \)\(11\!\cdots\!53\)\( T_{3}^{44} - \)\(41\!\cdots\!90\)\( T_{3}^{43} + \)\(28\!\cdots\!48\)\( T_{3}^{42} + \)\(16\!\cdots\!60\)\( T_{3}^{41} - \)\(60\!\cdots\!70\)\( T_{3}^{40} + \)\(11\!\cdots\!80\)\( T_{3}^{39} + \)\(11\!\cdots\!83\)\( T_{3}^{38} - \)\(50\!\cdots\!30\)\( T_{3}^{37} - \)\(18\!\cdots\!20\)\( T_{3}^{36} + \)\(13\!\cdots\!50\)\( T_{3}^{35} + \)\(23\!\cdots\!22\)\( T_{3}^{34} - \)\(25\!\cdots\!50\)\( T_{3}^{33} - \)\(22\!\cdots\!49\)\( T_{3}^{32} + \)\(35\!\cdots\!90\)\( T_{3}^{31} + \)\(18\!\cdots\!99\)\( T_{3}^{30} - \)\(45\!\cdots\!90\)\( T_{3}^{29} - \)\(33\!\cdots\!74\)\( T_{3}^{28} + \)\(43\!\cdots\!50\)\( T_{3}^{27} - \)\(16\!\cdots\!80\)\( T_{3}^{26} - \)\(23\!\cdots\!40\)\( T_{3}^{25} + \)\(22\!\cdots\!49\)\( T_{3}^{24} - \)\(32\!\cdots\!50\)\( T_{3}^{23} - \)\(12\!\cdots\!78\)\( T_{3}^{22} - \)\(22\!\cdots\!40\)\( T_{3}^{21} + \)\(21\!\cdots\!48\)\( T_{3}^{20} - \)\(20\!\cdots\!40\)\( T_{3}^{19} - \)\(42\!\cdots\!68\)\( T_{3}^{18} + \)\(14\!\cdots\!60\)\( T_{3}^{17} + \)\(36\!\cdots\!20\)\( T_{3}^{16} - \)\(25\!\cdots\!40\)\( T_{3}^{15} + \)\(44\!\cdots\!48\)\( T_{3}^{14} - \)\(48\!\cdots\!40\)\( T_{3}^{13} + \)\(49\!\cdots\!64\)\( T_{3}^{12} - \)\(21\!\cdots\!40\)\( T_{3}^{11} + \)\(30\!\cdots\!56\)\( T_{3}^{10} + \)\(45\!\cdots\!20\)\( T_{3}^{9} - \)\(53\!\cdots\!36\)\( T_{3}^{8} + \)\(40\!\cdots\!40\)\( T_{3}^{7} + \)\(49\!\cdots\!88\)\( T_{3}^{6} - \)\(32\!\cdots\!20\)\( T_{3}^{5} - 215404622848 T_{3}^{4} + 22720706560 T_{3}^{3} + 380170240 T_{3}^{2} + 1597440 T_{3} + 4096 \)">\(T_{3}^{96} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(950, [\chi])\).