Newform orbit 220.3.h.a

• Label: 220.3.h.a
• Level: $220$
• Weight: $3$
• Character orbit: 220.h
• Analytic conductor: $5.995$
• Analytic rank: $0$
• Dimension: $60$
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(5.99456581593\)
Analytic rank:	\(0\)
Dimension:	\(60\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 60 q - 4 q^{4} + 4 q^{5} + 12 q^{6} + 180 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
199.1	−1.99644	−	0.119294i	0.337678			3.97154	+	0.476326i	1.42257	+	4.79336i	−0.674153	−	0.0402829i	−6.79613			−7.87211	−	1.42474i	−8.88597			−2.26826	−	9.73935i
199.2	−1.99644	+	0.119294i	0.337678			3.97154	−	0.476326i	1.42257	−	4.79336i	−0.674153	+	0.0402829i	−6.79613			−7.87211	+	1.42474i	−8.88597			−2.26826	+	9.73935i
199.3	−1.97378	−	0.322758i	−4.73469			3.79165	+	1.27411i	−1.42827	+	4.79166i	9.34526	+	1.52816i	7.98176			−7.07268	−	3.73861i	13.4173			4.36565	−	8.99673i
199.4	−1.97378	+	0.322758i	−4.73469			3.79165	−	1.27411i	−1.42827	−	4.79166i	9.34526	−	1.52816i	7.98176			−7.07268	+	3.73861i	13.4173			4.36565	+	8.99673i
199.5	−1.87504	−	0.695850i	2.63169			3.03158	+	2.60950i	1.21581	−	4.84993i	−4.93453	−	1.83126i	12.3259			−3.86853	−	7.00246i	−2.07421			−5.65453	+	8.24781i
199.6	−1.87504	+	0.695850i	2.63169			3.03158	−	2.60950i	1.21581	+	4.84993i	−4.93453	+	1.83126i	12.3259			−3.86853	+	7.00246i	−2.07421			−5.65453	−	8.24781i
199.7	−1.80241	−	0.866788i	−2.17924			2.49736	+	3.12461i	4.97895	+	0.458348i	3.92787	+	1.88893i	1.79794			−1.79289	−	7.79651i	−4.25093			−8.57681	−	5.14182i
199.8	−1.80241	+	0.866788i	−2.17924			2.49736	−	3.12461i	4.97895	−	0.458348i	3.92787	−	1.88893i	1.79794			−1.79289	+	7.79651i	−4.25093			−8.57681	+	5.14182i
199.9	−1.77475	−	0.922089i	5.34862			2.29950	+	3.27296i	3.88532	+	3.14711i	−9.49248	−	4.93190i	−2.03277			−1.06309	−	7.92905i	19.6077			−3.99357	−	9.16795i
199.10	−1.77475	+	0.922089i	5.34862			2.29950	−	3.27296i	3.88532	−	3.14711i	−9.49248	+	4.93190i	−2.03277			−1.06309	+	7.92905i	19.6077			−3.99357	+	9.16795i
199.11	−1.76106	−	0.947973i	−3.26539			2.20269	+	3.33888i	−4.29635	−	2.55761i	5.75056	+	3.09550i	−7.75789			−0.713917	−	7.96808i	1.66278			5.14160	+	8.57694i
199.12	−1.76106	+	0.947973i	−3.26539			2.20269	−	3.33888i	−4.29635	+	2.55761i	5.75056	−	3.09550i	−7.75789			−0.713917	+	7.96808i	1.66278			5.14160	−	8.57694i
199.13	−1.58018	−	1.22598i	0.354051			0.993967	+	3.87454i	−4.79515	+	1.41652i	−0.559466	−	0.434058i	6.53369			3.17944	−	7.34106i	−8.87465			9.31385	+	3.64037i
199.14	−1.58018	+	1.22598i	0.354051			0.993967	−	3.87454i	−4.79515	−	1.41652i	−0.559466	+	0.434058i	6.53369			3.17944	+	7.34106i	−8.87465			9.31385	−	3.64037i
199.15	−1.24492	−	1.56530i	2.70048			−0.900339	+	3.89736i	−1.77924	+	4.67272i	−3.36188	−	4.22706i	−0.970912			7.22139	−	3.44260i	−1.70743			9.52923	−	3.03213i
199.16	−1.24492	+	1.56530i	2.70048			−0.900339	−	3.89736i	−1.77924	−	4.67272i	−3.36188	+	4.22706i	−0.970912			7.22139	+	3.44260i	−1.70743			9.52923	+	3.03213i
199.17	−1.20196	−	1.59852i	1.87168			−1.11056	+	3.84274i	3.84060	−	3.20153i	−2.24970	−	2.99193i	−11.6487			7.47757	−	2.84358i	−5.49681			−9.73399	−	2.29116i
199.18	−1.20196	+	1.59852i	1.87168			−1.11056	−	3.84274i	3.84060	+	3.20153i	−2.24970	+	2.99193i	−11.6487			7.47757	+	2.84358i	−5.49681			−9.73399	+	2.29116i
199.19	−1.02937	−	1.71476i	−4.39883			−1.88080	+	3.53024i	0.646763	+	4.95799i	4.52802	+	7.54293i	−6.76347			7.98955	−	0.408800i	10.3497			7.83601	−	6.21265i
199.20	−1.02937	+	1.71476i	−4.39883			−1.88080	−	3.53024i	0.646763	−	4.95799i	4.52802	−	7.54293i	−6.76347			7.98955	+	0.408800i	10.3497			7.83601	+	6.21265i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
4.b	odd	2	1	inner
5.b	even	2	1	inner
20.d	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	220.3.h.a	✓	60
4.b	odd	2	1	inner	220.3.h.a	✓	60
5.b	even	2	1	inner	220.3.h.a	✓	60
20.d	odd	2	1	inner	220.3.h.a	✓	60

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
220.3.h.a	✓	60	1.a	even	1	1	trivial
220.3.h.a	✓	60	4.b	odd	2	1	inner
220.3.h.a	✓	60	5.b	even	2	1	inner
220.3.h.a	✓	60	20.d	odd	2	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(220, [\chi])\).