Newform orbit 731.2.j.a

• Label: 731.2.j.a
• Level: $731$
• Weight: $2$
• Character orbit: 731.j
• Analytic conductor: $5.837$
• Analytic rank: $0$
• Dimension: $128$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.j (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.83706438776\)
Analytic rank:	\(0\)
Dimension:	\(128\)
Relative dimension:	\(64\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 128 q - 4 q^{2} + 116 q^{4} - 12 q^{8} + 70 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
135.1	−2.78045			−1.68248	−	0.971380i	5.73090			1.18797	+	0.685872i	4.67805	+	2.70087i	−2.90625	+	1.67793i	−10.3736			0.387158	+	0.670578i	−3.30308	−	1.90703i
135.2	−2.78045			1.68248	+	0.971380i	5.73090			−1.18797	−	0.685872i	−4.67805	−	2.70087i	2.90625	−	1.67793i	−10.3736			0.387158	+	0.670578i	3.30308	+	1.90703i
135.3	−2.53253			−1.51123	−	0.872510i	4.41371			−3.60596	−	2.08190i	3.82724	+	2.20966i	0.435566	−	0.251474i	−6.11280			0.0225487	+	0.0390554i	9.13221	+	5.27248i
135.4	−2.53253			1.51123	+	0.872510i	4.41371			3.60596	+	2.08190i	−3.82724	−	2.20966i	−0.435566	+	0.251474i	−6.11280			0.0225487	+	0.0390554i	−9.13221	−	5.27248i
135.5	−2.51145			−1.76122	−	1.01684i	4.30737			1.18626	+	0.684888i	4.42321	+	2.55374i	3.84346	−	2.21902i	−5.79485			0.567928	+	0.983681i	−2.97923	−	1.72006i
135.6	−2.51145			1.76122	+	1.01684i	4.30737			−1.18626	−	0.684888i	−4.42321	−	2.55374i	−3.84346	+	2.21902i	−5.79485			0.567928	+	0.983681i	2.97923	+	1.72006i
135.7	−2.11821			−2.72590	−	1.57380i	2.48683			−0.994359	−	0.574094i	5.77403	+	3.33364i	−0.0492215	+	0.0284181i	−1.03120			3.45368	+	5.98195i	2.10626	+	1.21605i
135.8	−2.11821			2.72590	+	1.57380i	2.48683			0.994359	+	0.574094i	−5.77403	−	3.33364i	0.0492215	−	0.0284181i	−1.03120			3.45368	+	5.98195i	−2.10626	−	1.21605i
135.9	−2.09187			−0.414315	−	0.239205i	2.37591			1.22310	+	0.706158i	0.866692	+	0.500385i	−2.02420	+	1.16867i	−0.786343			−1.38556	−	2.39986i	−2.55857	−	1.47719i
135.10	−2.09187			0.414315	+	0.239205i	2.37591			−1.22310	−	0.706158i	−0.866692	−	0.500385i	2.02420	−	1.16867i	−0.786343			−1.38556	−	2.39986i	2.55857	+	1.47719i
135.11	−2.05109			−2.62751	−	1.51699i	2.20698			2.73044	+	1.57642i	5.38926	+	3.11149i	0.592018	−	0.341802i	−0.424527			3.10253	+	5.37374i	−5.60038	−	3.23338i
135.12	−2.05109			2.62751	+	1.51699i	2.20698			−2.73044	−	1.57642i	−5.38926	−	3.11149i	−0.592018	+	0.341802i	−0.424527			3.10253	+	5.37374i	5.60038	+	3.23338i
135.13	−2.04963			−1.14468	−	0.660879i	2.20099			−1.07261	−	0.619273i	2.34616	+	1.35456i	0.325723	−	0.188056i	−0.411958			−0.626478	−	1.08509i	2.19846	+	1.26928i
135.14	−2.04963			1.14468	+	0.660879i	2.20099			1.07261	+	0.619273i	−2.34616	−	1.35456i	−0.325723	+	0.188056i	−0.411958			−0.626478	−	1.08509i	−2.19846	−	1.26928i
135.15	−1.73933			−1.10646	−	0.638817i	1.02526			2.28826	+	1.32113i	1.92450	+	1.11111i	−4.26158	+	2.46042i	1.69540			−0.683825	−	1.18442i	−3.98003	−	2.29787i
135.16	−1.73933			1.10646	+	0.638817i	1.02526			−2.28826	−	1.32113i	−1.92450	−	1.11111i	4.26158	−	2.46042i	1.69540			−0.683825	−	1.18442i	3.98003	+	2.29787i
135.17	−1.28957			−0.316022	−	0.182455i	−0.337012			3.24573	+	1.87392i	0.407532	+	0.235289i	2.23124	−	1.28820i	3.01374			−1.43342	−	2.48276i	−4.18560	−	2.41656i
135.18	−1.28957			0.316022	+	0.182455i	−0.337012			−3.24573	−	1.87392i	−0.407532	−	0.235289i	−2.23124	+	1.28820i	3.01374			−1.43342	−	2.48276i	4.18560	+	2.41656i
135.19	−1.28732			−1.78909	−	1.03293i	−0.342809			0.933959	+	0.539221i	2.30313	+	1.32971i	3.12985	−	1.80702i	3.01594			0.633889	+	1.09793i	−1.20230	−	0.694150i
135.20	−1.28732			1.78909	+	1.03293i	−0.342809			−0.933959	−	0.539221i	−2.30313	−	1.32971i	−3.12985	+	1.80702i	3.01594			0.633889	+	1.09793i	1.20230	+	0.694150i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
17.b	even	2	1	inner
43.c	even	3	1	inner
731.j	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	731.2.j.a	✓	128
17.b	even	2	1	inner	731.2.j.a	✓	128
43.c	even	3	1	inner	731.2.j.a	✓	128
731.j	even	6	1	inner	731.2.j.a	✓	128

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
731.2.j.a	✓	128	1.a	even	1	1	trivial
731.2.j.a	✓	128	17.b	even	2	1	inner
731.2.j.a	✓	128	43.c	even	3	1	inner
731.2.j.a	✓	128	731.j	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(731, [\chi])\).