Newform orbit 672.4.bb.a

• Label: 672.4.bb.a
• Level: $672$
• Weight: $4$
• Character orbit: 672.bb
• Analytic conductor: $39.649$
• Analytic rank: $0$
• Dimension: $96$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	672.bb (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(39.6492835239\)
Analytic rank:	\(0\)
Dimension:	\(96\)
Relative dimension:	\(48\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 168)
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.

\(\operatorname{Tr}(f)(q) = \) \( 96 q + 432 q^{9} - 40 q^{11} - 1200 q^{25} - 456 q^{35} + 1616 q^{43} - 360 q^{49} - 336 q^{57} - 4128 q^{59} + 1440 q^{67} - 648 q^{73} - 3888 q^{81} + 104 q^{91} - 720 q^{99}+O(q^{100}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
271.1		0		−2.59808	+	1.50000i		0		−4.82508	+	8.35729i		0		14.2799	−	11.7934i		0		4.50000	−	7.79423i		0
271.2		0		−2.59808	+	1.50000i		0		4.82508	−	8.35729i		0		−14.2799	+	11.7934i		0		4.50000	−	7.79423i		0
271.3		0		−2.59808	+	1.50000i		0		−4.08960	+	7.08340i		0		−18.1007	−	3.91988i		0		4.50000	−	7.79423i		0
271.4		0		−2.59808	+	1.50000i		0		4.08960	−	7.08340i		0		18.1007	+	3.91988i		0		4.50000	−	7.79423i		0
271.5		0		−2.59808	+	1.50000i		0		−3.56336	+	6.17193i		0		−16.0311	+	9.27388i		0		4.50000	−	7.79423i		0
271.6		0		−2.59808	+	1.50000i		0		3.56336	−	6.17193i		0		16.0311	−	9.27388i		0		4.50000	−	7.79423i		0
271.7		0		−2.59808	+	1.50000i		0		−1.10134	+	1.90757i		0		−7.13695	+	17.0899i		0		4.50000	−	7.79423i		0
271.8		0		−2.59808	+	1.50000i		0		1.10134	−	1.90757i		0		7.13695	−	17.0899i		0		4.50000	−	7.79423i		0
271.9		0		−2.59808	+	1.50000i		0		−2.37912	+	4.12075i		0		−11.6311	−	14.4124i		0		4.50000	−	7.79423i		0
271.10		0		−2.59808	+	1.50000i		0		2.37912	−	4.12075i		0		11.6311	+	14.4124i		0		4.50000	−	7.79423i		0
271.11		0		−2.59808	+	1.50000i		0		−4.53700	+	7.85831i		0		18.3201	+	2.71568i		0		4.50000	−	7.79423i		0
271.12		0		−2.59808	+	1.50000i		0		4.53700	−	7.85831i		0		−18.3201	−	2.71568i		0		4.50000	−	7.79423i		0
271.13		0		−2.59808	+	1.50000i		0		−6.00810	+	10.4063i		0		−8.17074	+	16.6204i		0		4.50000	−	7.79423i		0
271.14		0		−2.59808	+	1.50000i		0		6.00810	−	10.4063i		0		8.17074	−	16.6204i		0		4.50000	−	7.79423i		0
271.15		0		−2.59808	+	1.50000i		0		−6.01586	+	10.4198i		0		−9.34266	+	15.9911i		0		4.50000	−	7.79423i		0
271.16		0		−2.59808	+	1.50000i		0		6.01586	−	10.4198i		0		9.34266	−	15.9911i		0		4.50000	−	7.79423i		0
271.17		0		−2.59808	+	1.50000i		0		−7.16825	+	12.4158i		0		12.0691	+	14.0477i		0		4.50000	−	7.79423i		0
271.18		0		−2.59808	+	1.50000i		0		7.16825	−	12.4158i		0		−12.0691	−	14.0477i		0		4.50000	−	7.79423i		0
271.19		0		−2.59808	+	1.50000i		0		−7.30307	+	12.6493i		0		0.782311	−	18.5037i		0		4.50000	−	7.79423i		0
271.20		0		−2.59808	+	1.50000i		0		7.30307	−	12.6493i		0		−0.782311	+	18.5037i		0		4.50000	−	7.79423i		0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
7.d	odd	6	1	inner
8.d	odd	2	1	inner
56.m	even	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	672.4.bb.a		96
4.b	odd	2	1		168.4.t.a	✓	96
7.d	odd	6	1	inner	672.4.bb.a		96
8.b	even	2	1		168.4.t.a	✓	96
8.d	odd	2	1	inner	672.4.bb.a		96
28.f	even	6	1		168.4.t.a	✓	96
56.j	odd	6	1		168.4.t.a	✓	96
56.m	even	6	1	inner	672.4.bb.a		96

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
168.4.t.a	✓	96	4.b	odd	2	1
168.4.t.a	✓	96	8.b	even	2	1
168.4.t.a	✓	96	28.f	even	6	1
168.4.t.a	✓	96	56.j	odd	6	1
672.4.bb.a		96	1.a	even	1	1	trivial
672.4.bb.a		96	7.d	odd	6	1	inner
672.4.bb.a		96	8.d	odd	2	1	inner
672.4.bb.a		96	56.m	even	6	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{4}^{\mathrm{new}}(672, [\chi])\).