Newform orbit 280.2.n.b

• Label: 280.2.n.b
• Level: $280$
• Weight: $2$
• Character orbit: 280.n
• Analytic conductor: $2.236$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.n (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(2.23581125660\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 40 q - 12 q^{4} + 40 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
139.1	−1.27891	−	0.603655i	−1.64952			1.27120	+	1.54404i	−1.78913	−	1.34127i	2.10957	+	0.995738i	−0.157160	+	2.64108i	−0.693682	−	2.74204i	−0.279099			1.47847	+	2.79538i
139.2	−1.27891	−	0.603655i	1.64952			1.27120	+	1.54404i	1.78913	+	1.34127i	−2.10957	−	0.995738i	−0.157160	−	2.64108i	−0.693682	−	2.74204i	−0.279099			−1.47847	−	2.79538i
139.3	−1.27891	+	0.603655i	−1.64952			1.27120	−	1.54404i	−1.78913	+	1.34127i	2.10957	−	0.995738i	−0.157160	−	2.64108i	−0.693682	+	2.74204i	−0.279099			1.47847	−	2.79538i
139.4	−1.27891	+	0.603655i	1.64952			1.27120	−	1.54404i	1.78913	−	1.34127i	−2.10957	+	0.995738i	−0.157160	+	2.64108i	−0.693682	+	2.74204i	−0.279099			−1.47847	+	2.79538i
139.5	−1.20452	−	0.741038i	−2.57969			0.901725	+	1.78519i	−0.460102	+	2.18822i	3.10728	+	1.91165i	2.31487	−	1.28116i	0.236748	−	2.81850i	3.65479			2.17576	−	2.29480i
139.6	−1.20452	−	0.741038i	2.57969			0.901725	+	1.78519i	0.460102	−	2.18822i	−3.10728	−	1.91165i	2.31487	+	1.28116i	0.236748	−	2.81850i	3.65479			−2.17576	+	2.29480i
139.7	−1.20452	+	0.741038i	−2.57969			0.901725	−	1.78519i	−0.460102	−	2.18822i	3.10728	−	1.91165i	2.31487	+	1.28116i	0.236748	+	2.81850i	3.65479			2.17576	+	2.29480i
139.8	−1.20452	+	0.741038i	2.57969			0.901725	−	1.78519i	0.460102	+	2.18822i	−3.10728	+	1.91165i	2.31487	−	1.28116i	0.236748	+	2.81850i	3.65479			−2.17576	−	2.29480i
139.9	−0.918230	−	1.07557i	−1.19038			−0.313707	+	1.97524i	2.22369	−	0.234978i	1.09304	+	1.28034i	−2.11797	+	1.58562i	2.41257	−	1.47631i	−1.58299			−2.29459	−	2.17597i
139.10	−0.918230	−	1.07557i	1.19038			−0.313707	+	1.97524i	−2.22369	+	0.234978i	−1.09304	−	1.28034i	−2.11797	−	1.58562i	2.41257	−	1.47631i	−1.58299			2.29459	+	2.17597i
139.11	−0.918230	+	1.07557i	−1.19038			−0.313707	−	1.97524i	2.22369	+	0.234978i	1.09304	−	1.28034i	−2.11797	−	1.58562i	2.41257	+	1.47631i	−1.58299			−2.29459	+	2.17597i
139.12	−0.918230	+	1.07557i	1.19038			−0.313707	−	1.97524i	−2.22369	−	0.234978i	−1.09304	+	1.28034i	−2.11797	+	1.58562i	2.41257	+	1.47631i	−1.58299			2.29459	−	2.17597i
139.13	−0.510308	−	1.31893i	−0.857983			−1.47917	+	1.34612i	1.33029	−	1.79731i	0.437835	+	1.13162i	2.41097	−	1.08959i	2.53028	+	1.26399i	−2.26387			−3.04939	−	0.837376i
139.14	−0.510308	−	1.31893i	0.857983			−1.47917	+	1.34612i	−1.33029	+	1.79731i	−0.437835	−	1.13162i	2.41097	+	1.08959i	2.53028	+	1.26399i	−2.26387			3.04939	+	0.837376i
139.15	−0.510308	+	1.31893i	−0.857983			−1.47917	−	1.34612i	1.33029	+	1.79731i	0.437835	−	1.13162i	2.41097	+	1.08959i	2.53028	−	1.26399i	−2.26387			−3.04939	+	0.837376i
139.16	−0.510308	+	1.31893i	0.857983			−1.47917	−	1.34612i	−1.33029	−	1.79731i	−0.437835	+	1.13162i	2.41097	−	1.08959i	2.53028	−	1.26399i	−2.26387			3.04939	−	0.837376i
139.17	−0.244900	−	1.39285i	−2.91053			−1.88005	+	0.682218i	−1.83654	−	1.27559i	0.712789	+	4.05392i	−1.52252	−	2.16378i	1.41065	+	2.45154i	5.47117			−1.32694	+	2.87041i
139.18	−0.244900	−	1.39285i	2.91053			−1.88005	+	0.682218i	1.83654	+	1.27559i	−0.712789	−	4.05392i	−1.52252	+	2.16378i	1.41065	+	2.45154i	5.47117			1.32694	−	2.87041i
139.19	−0.244900	+	1.39285i	−2.91053			−1.88005	−	0.682218i	−1.83654	+	1.27559i	0.712789	−	4.05392i	−1.52252	+	2.16378i	1.41065	−	2.45154i	5.47117			−1.32694	−	2.87041i
139.20	−0.244900	+	1.39285i	2.91053			−1.88005	−	0.682218i	1.83654	−	1.27559i	−0.712789	+	4.05392i	−1.52252	−	2.16378i	1.41065	−	2.45154i	5.47117			1.32694	+	2.87041i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
7.b	odd	2	1	inner
8.d	odd	2	1	inner
35.c	odd	2	1	inner
40.e	odd	2	1	inner
56.e	even	2	1	inner
280.n	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	280.2.n.b	✓	40
4.b	odd	2	1		1120.2.n.b		40
5.b	even	2	1	inner	280.2.n.b	✓	40
7.b	odd	2	1	inner	280.2.n.b	✓	40
8.b	even	2	1		1120.2.n.b		40
8.d	odd	2	1	inner	280.2.n.b	✓	40
20.d	odd	2	1		1120.2.n.b		40
28.d	even	2	1		1120.2.n.b		40
35.c	odd	2	1	inner	280.2.n.b	✓	40
40.e	odd	2	1	inner	280.2.n.b	✓	40
40.f	even	2	1		1120.2.n.b		40
56.e	even	2	1	inner	280.2.n.b	✓	40
56.h	odd	2	1		1120.2.n.b		40
140.c	even	2	1		1120.2.n.b		40
280.c	odd	2	1		1120.2.n.b		40
280.n	even	2	1	inner	280.2.n.b	✓	40

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
280.2.n.b	✓	40	1.a	even	1	1	trivial
280.2.n.b	✓	40	5.b	even	2	1	inner
280.2.n.b	✓	40	7.b	odd	2	1	inner
280.2.n.b	✓	40	8.d	odd	2	1	inner
280.2.n.b	✓	40	35.c	odd	2	1	inner
280.2.n.b	✓	40	40.e	odd	2	1	inner
280.2.n.b	✓	40	56.e	even	2	1	inner
280.2.n.b	✓	40	280.n	even	2	1	inner
1120.2.n.b		40	4.b	odd	2	1
1120.2.n.b		40	8.b	even	2	1
1120.2.n.b		40	20.d	odd	2	1
1120.2.n.b		40	28.d	even	2	1
1120.2.n.b		40	40.f	even	2	1
1120.2.n.b		40	56.h	odd	2	1
1120.2.n.b		40	140.c	even	2	1
1120.2.n.b		40	280.c	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{10} - 20T_{3}^{8} + 137T_{3}^{6} - 382T_{3}^{4} + 432T_{3}^{2} - 160 \) acting on \(S_{2}^{\mathrm{new}}(280, [\chi])\).