Newform orbit 950.2.bb.d

• Label: 950.2.bb.d
• Level: $950$
• Weight: $2$
• Character orbit: 950.bb
• Analytic conductor: $7.586$
• Analytic rank: $0$
• Dimension: $96$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.bb (of order \(36\), degree \(12\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.58578819202\)
Analytic rank:	\(0\)
Dimension:	\(96\)
Relative dimension:	\(8\) over \(\Q(\zeta_{36})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96q - 12q^{6} + O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
143.1	−0.573576	+	0.819152i	−0.282278	+	3.22645i	−0.342020	−	0.939693i		0		−2.48104	−	2.08184i	−0.0261014	−	0.0974119i	0.965926	+	0.258819i	−7.37587	−	1.30056i		0
143.2	−0.573576	+	0.819152i	−0.0476128	+	0.544217i	−0.342020	−	0.939693i		0		−0.418487	−	0.351152i	−0.123323	−	0.460247i	0.965926	+	0.258819i	2.66052	+	0.469121i		0
143.3	−0.573576	+	0.819152i	0.134247	−	1.53445i	−0.342020	−	0.939693i		0		1.17995	+	0.990096i	−1.26063	−	4.70472i	0.965926	+	0.258819i	0.617895	+	0.108952i		0
143.4	−0.573576	+	0.819152i	0.225912	−	2.58219i	−0.342020	−	0.939693i		0		1.98563	+	1.66614i	0.690517	+	2.57704i	0.965926	+	0.258819i	−3.66223	−	0.645749i		0
143.5	0.573576	−	0.819152i	−0.225912	+	2.58219i	−0.342020	−	0.939693i		0		1.98563	+	1.66614i	−0.690517	−	2.57704i	−0.965926	−	0.258819i	−3.66223	−	0.645749i		0
143.6	0.573576	−	0.819152i	−0.134247	+	1.53445i	−0.342020	−	0.939693i		0		1.17995	+	0.990096i	1.26063	+	4.70472i	−0.965926	−	0.258819i	0.617895	+	0.108952i		0
143.7	0.573576	−	0.819152i	0.0476128	−	0.544217i	−0.342020	−	0.939693i		0		−0.418487	−	0.351152i	0.123323	+	0.460247i	−0.965926	−	0.258819i	2.66052	+	0.469121i		0
143.8	0.573576	−	0.819152i	0.282278	−	3.22645i	−0.342020	−	0.939693i		0		−2.48104	−	2.08184i	0.0261014	+	0.0974119i	−0.965926	−	0.258819i	−7.37587	−	1.30056i		0
193.1	−0.0871557	−	0.996195i	−1.07287	+	2.30077i	−0.984808	+	0.173648i		0		2.38552	+	0.868257i	3.67829	+	0.985594i	0.258819	+	0.965926i	−2.21412	−	2.63869i		0
193.2	−0.0871557	−	0.996195i	−0.0142429	+	0.0305440i	−0.984808	+	0.173648i		0		0.0316692	+	0.0115266i	−2.42021	−	0.648494i	0.258819	+	0.965926i	1.92763	+	2.29726i		0
193.3	−0.0871557	−	0.996195i	0.368687	−	0.790651i	−0.984808	+	0.173648i		0		−0.819776	−	0.298374i	1.54311	+	0.413475i	0.258819	+	0.965926i	1.43916	+	1.71513i		0
193.4	−0.0871557	−	0.996195i	1.36591	−	2.92920i	−0.984808	+	0.173648i		0		−3.03710	−	1.10542i	2.44739	+	0.655775i	0.258819	+	0.965926i	−4.78616	−	5.70392i		0
193.5	0.0871557	+	0.996195i	−1.36591	+	2.92920i	−0.984808	+	0.173648i		0		−3.03710	−	1.10542i	−2.44739	−	0.655775i	−0.258819	−	0.965926i	−4.78616	−	5.70392i		0
193.6	0.0871557	+	0.996195i	−0.368687	+	0.790651i	−0.984808	+	0.173648i		0		−0.819776	−	0.298374i	−1.54311	−	0.413475i	−0.258819	−	0.965926i	1.43916	+	1.71513i		0
193.7	0.0871557	+	0.996195i	0.0142429	−	0.0305440i	−0.984808	+	0.173648i		0		0.0316692	+	0.0115266i	2.42021	+	0.648494i	−0.258819	−	0.965926i	1.92763	+	2.29726i		0
193.8	0.0871557	+	0.996195i	1.07287	−	2.30077i	−0.984808	+	0.173648i		0		2.38552	+	0.868257i	−3.67829	−	0.985594i	−0.258819	−	0.965926i	−2.21412	−	2.63869i		0
243.1	−0.422618	−	0.906308i	−2.62162	−	1.83568i	−0.642788	+	0.766044i		0		−0.555745	+	3.15179i	−0.894036	−	3.33659i	0.965926	+	0.258819i	2.47712	+	6.80584i		0
243.2	−0.422618	−	0.906308i	−1.05824	−	0.740990i	−0.642788	+	0.766044i		0		−0.224332	+	1.27225i	1.24089	+	4.63106i	0.965926	+	0.258819i	−0.455247	−	1.25078i		0
243.3	−0.422618	−	0.906308i	0.451001	+	0.315794i	−0.642788	+	0.766044i		0		0.0956055	−	0.542206i	−0.410083	−	1.53045i	0.965926	+	0.258819i	−0.922385	−	2.53423i		0
243.4	−0.422618	−	0.906308i	1.68936	+	1.18290i	−0.642788	+	0.766044i		0		0.358120	−	2.03100i	−0.500613	−	1.86831i	0.965926	+	0.258819i	0.428624	+	1.17763i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
5.c	odd	4	2	inner
19.f	odd	18	1	inner
95.o	odd	18	1	inner
95.r	even	36	2	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	950.2.bb.d	✓	96
5.b	even	2	1	inner	950.2.bb.d	✓	96
5.c	odd	4	2	inner	950.2.bb.d	✓	96
19.f	odd	18	1	inner	950.2.bb.d	✓	96
95.o	odd	18	1	inner	950.2.bb.d	✓	96
95.r	even	36	2	inner	950.2.bb.d	✓	96

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
950.2.bb.d	✓	96	1.a	even	1	1	trivial
950.2.bb.d	✓	96	5.b	even	2	1	inner
950.2.bb.d	✓	96	5.c	odd	4	2	inner
950.2.bb.d	✓	96	19.f	odd	18	1	inner
950.2.bb.d	✓	96	95.o	odd	18	1	inner
950.2.bb.d	✓	96	95.r	even	36	2	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(16\!\cdots\!60\)\( T_{3}^{72} - \)\(78\!\cdots\!33\)\( T_{3}^{68} + \)\(17\!\cdots\!38\)\( T_{3}^{64} - \)\(11\!\cdots\!83\)\( T_{3}^{60} + \)\(24\!\cdots\!81\)\( T_{3}^{56} + \)\(84\!\cdots\!87\)\( T_{3}^{52} + \)\(12\!\cdots\!20\)\( T_{3}^{48} - \)\(11\!\cdots\!20\)\( T_{3}^{44} - \)\(66\!\cdots\!12\)\( T_{3}^{40} + \)\(11\!\cdots\!01\)\( T_{3}^{36} + \)\(46\!\cdots\!74\)\( T_{3}^{32} + \)\(11\!\cdots\!49\)\( T_{3}^{28} + \)\(14\!\cdots\!21\)\( T_{3}^{24} - \)\(50\!\cdots\!08\)\( T_{3}^{20} - \)\(10\!\cdots\!24\)\( T_{3}^{16} - \)\(35\!\cdots\!80\)\( T_{3}^{12} + \)\(10\!\cdots\!96\)\( T_{3}^{8} + \)\(45\!\cdots\!92\)\( T_{3}^{4} + 16777216 \)">\(T_{3}^{96} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(950, [\chi])\).