Newform orbit 68.3.j.a

• Label: 68.3.j.a
• Level: $68$
• Weight: $3$
• Character orbit: 68.j
• Analytic conductor: $1.853$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 68 = 2^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	68.j (of order \(16\), degree \(8\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(1.85286579765\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(3\) over \(\Q(\zeta_{16})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
5.1		0		−1.38851	−	2.07805i		0		0.644765	−	3.24145i		0		−1.30222	−	6.54672i		0		1.05382	−	2.54414i		0
5.2		0		1.14983	+	1.72085i		0		−1.62932	+	8.19112i		0		−0.438485	−	2.20441i		0		1.80495	−	4.35753i		0
5.3		0		2.41825	+	3.61917i		0		1.46749	−	7.37755i		0		2.39103	+	12.0205i		0		−3.80631	+	9.18925i		0
29.1		0		−3.10706	+	2.07607i		0		−3.56513	−	0.709149i		0		−8.68444	+	1.72744i		0		1.89958	−	4.58600i		0
29.2		0		−0.217350	+	0.145228i		0		3.17077	+	0.630706i		0		11.7946	−	2.34609i		0		−3.41800	+	8.25179i		0
29.3		0		3.97325	−	2.65484i		0		1.32564	+	0.263686i		0		−8.00313	+	1.59192i		0		5.29439	−	12.7818i		0
37.1		0		−4.36068	−	0.867393i		0		5.40818	+	8.09391i		0		−3.55932	+	5.32690i		0		9.94825	+	4.12070i		0
37.2		0		−2.30187	−	0.457871i		0		−3.78183	−	5.65992i		0		6.79797	−	10.1739i		0		−3.22593	−	1.33623i		0
37.3		0		3.40058	+	0.676418i		0		0.820872	+	1.22852i		0		0.0307230	−	0.0459802i		0		2.79151	+	1.15628i		0
41.1		0		−1.38851	+	2.07805i		0		0.644765	+	3.24145i		0		−1.30222	+	6.54672i		0		1.05382	+	2.54414i		0
41.2		0		1.14983	−	1.72085i		0		−1.62932	−	8.19112i		0		−0.438485	+	2.20441i		0		1.80495	+	4.35753i		0
41.3		0		2.41825	−	3.61917i		0		1.46749	+	7.37755i		0		2.39103	−	12.0205i		0		−3.80631	−	9.18925i		0
45.1		0		−0.587613	−	2.95413i		0		−6.91487	−	4.62037i		0		−0.359295	+	0.240073i		0		−0.0666833	+	0.0276211i		0
45.2		0		−0.0679565	−	0.341640i		0		4.95843	+	3.31311i		0		2.89267	−	1.93282i		0		8.20282	−	3.39772i		0
45.3		0		1.08912	+	5.47535i		0		−1.90499	−	1.27287i		0		−1.56010	+	1.04243i		0		−20.4784	+	8.48243i		0
57.1		0		−4.36068	+	0.867393i		0		5.40818	−	8.09391i		0		−3.55932	−	5.32690i		0		9.94825	−	4.12070i		0
57.2		0		−2.30187	+	0.457871i		0		−3.78183	+	5.65992i		0		6.79797	+	10.1739i		0		−3.22593	+	1.33623i		0
57.3		0		3.40058	−	0.676418i		0		0.820872	−	1.22852i		0		0.0307230	+	0.0459802i		0		2.79151	−	1.15628i		0
61.1		0		−3.10706	−	2.07607i		0		−3.56513	+	0.709149i		0		−8.68444	−	1.72744i		0		1.89958	+	4.58600i		0
61.2		0		−0.217350	−	0.145228i		0		3.17077	−	0.630706i		0		11.7946	+	2.34609i		0		−3.41800	−	8.25179i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
17.e	odd	16	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	68.3.j.a	✓	24
4.b	odd	2	1		272.3.bh.e		24
17.e	odd	16	1	inner	68.3.j.a	✓	24
68.i	even	16	1		272.3.bh.e		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
68.3.j.a	✓	24	1.a	even	1	1	trivial
68.3.j.a	✓	24	17.e	odd	16	1	inner
272.3.bh.e		24	4.b	odd	2	1
272.3.bh.e		24	68.i	even	16	1

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(68, [\chi])\).