Newform orbit 220.2.g.b

• Label: 220.2.g.b
• Level: $220$
• Weight: $2$
• Character orbit: 220.g
• Analytic conductor: $1.757$
• Analytic rank: $0$
• Dimension: $24$
• Inner twists: $8$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(1.75670884447\)
Analytic rank:	\(0\)
Dimension:	\(24\)
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.

\(\operatorname{Tr}(f)(q) = \) 24 * q - 4 * q^4 - 4 * q^5 + 40 * q^9 + 12 * q^14 - 12 * q^16 - 20 * q^20 - 36 * q^25 - 48 * q^26 + 28 * q^34 - 48 * q^36 + 56 * q^44 - 48 * q^45 + 48 * q^49 + 20 * q^56 - 8 * q^60 + 20 * q^64 - 52 * q^66 - 8 * q^69 - 64 * q^70 + 64 * q^80 - 104 * q^81 + 72 * q^86 - 16 * q^89

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
219.1	−1.33078	−	0.478573i	−1.30496			1.54194	+	1.27375i	−0.393401	+	2.20119i	1.73662	+	0.624520i		−	1.57789i	−1.44239	−	2.43300i	−1.29707			1.57696	−	2.74102i
219.2	−1.33078	−	0.478573i	1.30496			1.54194	+	1.27375i	−0.393401	−	2.20119i	−1.73662	−	0.624520i		−	1.57789i	−1.44239	−	2.43300i	−1.29707			−0.529900	+	3.11756i
219.3	−1.33078	+	0.478573i	−1.30496			1.54194	−	1.27375i	−0.393401	−	2.20119i	1.73662	−	0.624520i			1.57789i	−1.44239	+	2.43300i	−1.29707			1.57696	+	2.74102i
219.4	−1.33078	+	0.478573i	1.30496			1.54194	−	1.27375i	−0.393401	+	2.20119i	−1.73662	+	0.624520i			1.57789i	−1.44239	+	2.43300i	−1.29707			−0.529900	−	3.11756i
219.5	−0.896270	−	1.09394i	−2.84322			−0.393401	+	1.96093i	−1.64854	−	1.51074i	2.54829	+	3.11030i			3.37357i	2.49773	−	1.32716i	5.08387			−0.175122	+	3.15742i
219.6	−0.896270	−	1.09394i	2.84322			−0.393401	+	1.96093i	−1.64854	+	1.51074i	−2.54829	−	3.11030i			3.37357i	2.49773	−	1.32716i	5.08387			3.13019	+	0.449366i
219.7	−0.896270	+	1.09394i	−2.84322			−0.393401	−	1.96093i	−1.64854	+	1.51074i	2.54829	−	3.11030i		−	3.37357i	2.49773	+	1.32716i	5.08387			−0.175122	−	3.15742i
219.8	−0.896270	+	1.09394i	2.84322			−0.393401	−	1.96093i	−1.64854	−	1.51074i	−2.54829	+	3.11030i		−	3.37357i	2.49773	+	1.32716i	5.08387			3.13019	−	0.449366i
219.9	−0.419204	−	1.35065i	−2.05261			−1.64854	+	1.13240i	1.54194	+	1.61939i	0.860462	+	2.77236i		−	1.06270i	2.22056	+	1.75189i	1.21320			1.54085	−	2.76148i
219.10	−0.419204	−	1.35065i	2.05261			−1.64854	+	1.13240i	1.54194	−	1.61939i	−0.860462	−	2.77236i		−	1.06270i	2.22056	+	1.75189i	1.21320			−2.83363	−	1.40377i
219.11	−0.419204	+	1.35065i	−2.05261			−1.64854	−	1.13240i	1.54194	−	1.61939i	0.860462	−	2.77236i			1.06270i	2.22056	−	1.75189i	1.21320			1.54085	+	2.76148i
219.12	−0.419204	+	1.35065i	2.05261			−1.64854	−	1.13240i	1.54194	+	1.61939i	−0.860462	+	2.77236i			1.06270i	2.22056	−	1.75189i	1.21320			−2.83363	+	1.40377i
219.13	0.419204	−	1.35065i	−2.05261			−1.64854	−	1.13240i	1.54194	−	1.61939i	−0.860462	+	2.77236i		−	1.06270i	−2.22056	+	1.75189i	1.21320			−1.54085	−	2.76148i
219.14	0.419204	−	1.35065i	2.05261			−1.64854	−	1.13240i	1.54194	+	1.61939i	0.860462	−	2.77236i		−	1.06270i	−2.22056	+	1.75189i	1.21320			2.83363	−	1.40377i
219.15	0.419204	+	1.35065i	−2.05261			−1.64854	+	1.13240i	1.54194	+	1.61939i	−0.860462	−	2.77236i			1.06270i	−2.22056	−	1.75189i	1.21320			−1.54085	+	2.76148i
219.16	0.419204	+	1.35065i	2.05261			−1.64854	+	1.13240i	1.54194	−	1.61939i	0.860462	+	2.77236i			1.06270i	−2.22056	−	1.75189i	1.21320			2.83363	+	1.40377i
219.17	0.896270	−	1.09394i	−2.84322			−0.393401	−	1.96093i	−1.64854	+	1.51074i	−2.54829	+	3.11030i			3.37357i	−2.49773	−	1.32716i	5.08387			0.175122	+	3.15742i
219.18	0.896270	−	1.09394i	2.84322			−0.393401	−	1.96093i	−1.64854	−	1.51074i	2.54829	−	3.11030i			3.37357i	−2.49773	−	1.32716i	5.08387			−3.13019	+	0.449366i
219.19	0.896270	+	1.09394i	−2.84322			−0.393401	+	1.96093i	−1.64854	−	1.51074i	−2.54829	−	3.11030i		−	3.37357i	−2.49773	+	1.32716i	5.08387			0.175122	−	3.15742i
219.20	0.896270	+	1.09394i	2.84322			−0.393401	+	1.96093i	−1.64854	+	1.51074i	2.54829	+	3.11030i		−	3.37357i	−2.49773	+	1.32716i	5.08387			−3.13019	−	0.449366i

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
11.b	odd	2	1	inner
20.d	odd	2	1	inner
44.c	even	2	1	inner
55.d	odd	2	1	inner
220.g	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	220.2.g.b	✓	24
4.b	odd	2	1	inner	220.2.g.b	✓	24
5.b	even	2	1	inner	220.2.g.b	✓	24
11.b	odd	2	1	inner	220.2.g.b	✓	24
20.d	odd	2	1	inner	220.2.g.b	✓	24
44.c	even	2	1	inner	220.2.g.b	✓	24
55.d	odd	2	1	inner	220.2.g.b	✓	24
220.g	even	2	1	inner	220.2.g.b	✓	24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
220.2.g.b	✓	24	1.a	even	1	1	trivial
220.2.g.b	✓	24	4.b	odd	2	1	inner
220.2.g.b	✓	24	5.b	even	2	1	inner
220.2.g.b	✓	24	11.b	odd	2	1	inner
220.2.g.b	✓	24	20.d	odd	2	1	inner
220.2.g.b	✓	24	44.c	even	2	1	inner
220.2.g.b	✓	24	55.d	odd	2	1	inner
220.2.g.b	✓	24	220.g	even	2	1	inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{6} - 14T_{3}^{4} + 55T_{3}^{2} - 58 \) acting on \(S_{2}^{\mathrm{new}}(220, [\chi])\).