Newform orbit 935.2.p.a

• Label: 935.2.p.a
• Level: $935$
• Weight: $2$
• Character orbit: 935.p
• Analytic conductor: $7.466$
• Analytic rank: $0$
• Dimension: $208$
• CM: no
• Inner twists: $8$

Newspace parameters

Level:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.p (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.46601258899\)
Analytic rank:	\(0\)
Dimension:	\(208\)
Relative dimension:	\(104\) over \(\Q(i)\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 208 q+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
373.1	−1.93457	−	1.93457i	−1.97040	+	1.97040i			5.48513i	−1.84480	+	1.26362i	7.62377			−3.21639	+	3.21639i	6.74223	−	6.74223i		−	4.76498i	6.01345	+	1.12433i
373.2	−1.93457	−	1.93457i	1.97040	−	1.97040i			5.48513i	1.84480	−	1.26362i	−7.62377			3.21639	−	3.21639i	6.74223	−	6.74223i		−	4.76498i	−6.01345	−	1.12433i
373.3	−1.90074	−	1.90074i	−0.908745	+	0.908745i			5.22565i	0.0124139	−	2.23603i	3.45458			−0.0277813	+	0.0277813i	6.13113	−	6.13113i			1.34837i	−4.27372	+	4.22653i
373.4	−1.90074	−	1.90074i	0.908745	−	0.908745i			5.22565i	−0.0124139	+	2.23603i	−3.45458			0.0277813	−	0.0277813i	6.13113	−	6.13113i			1.34837i	4.27372	−	4.22653i
373.5	−1.79176	−	1.79176i	−1.80590	+	1.80590i			4.42078i	1.15216	+	1.91639i	6.47147			2.12879	−	2.12879i	4.33746	−	4.33746i		−	3.52256i	1.36931	−	5.49808i
373.6	−1.79176	−	1.79176i	1.80590	−	1.80590i			4.42078i	−1.15216	−	1.91639i	−6.47147			−2.12879	+	2.12879i	4.33746	−	4.33746i		−	3.52256i	−1.36931	+	5.49808i
373.7	−1.77657	−	1.77657i	−0.973550	+	0.973550i			4.31239i	2.19071	−	0.448092i	3.45916			1.16367	−	1.16367i	4.10812	−	4.10812i			1.10440i	−4.68801	−	3.09588i
373.8	−1.77657	−	1.77657i	0.973550	−	0.973550i			4.31239i	−2.19071	+	0.448092i	−3.45916			−1.16367	+	1.16367i	4.10812	−	4.10812i			1.10440i	4.68801	+	3.09588i
373.9	−1.72288	−	1.72288i	−0.866900	+	0.866900i			3.93664i	2.10810	+	0.745601i	2.98713			−3.35384	+	3.35384i	3.33660	−	3.33660i			1.49697i	−2.34742	−	4.91659i
373.10	−1.72288	−	1.72288i	0.866900	−	0.866900i			3.93664i	−2.10810	−	0.745601i	−2.98713			3.35384	−	3.35384i	3.33660	−	3.33660i			1.49697i	2.34742	+	4.91659i
373.11	−1.68384	−	1.68384i	−0.306356	+	0.306356i			3.67067i	−0.482021	+	2.18350i	1.03171			0.744260	−	0.744260i	2.81314	−	2.81314i			2.81229i	4.48832	−	2.86502i
373.12	−1.68384	−	1.68384i	0.306356	−	0.306356i			3.67067i	0.482021	−	2.18350i	−1.03171			−0.744260	+	0.744260i	2.81314	−	2.81314i			2.81229i	−4.48832	+	2.86502i
373.13	−1.63949	−	1.63949i	−2.37314	+	2.37314i			3.37583i	−0.615758	−	2.14961i	7.78145			2.14658	−	2.14658i	2.25565	−	2.25565i		−	8.26358i	−2.51474	+	4.53379i
373.14	−1.63949	−	1.63949i	2.37314	−	2.37314i			3.37583i	0.615758	+	2.14961i	−7.78145			−2.14658	+	2.14658i	2.25565	−	2.25565i		−	8.26358i	2.51474	−	4.53379i
373.15	−1.49933	−	1.49933i	−1.63420	+	1.63420i			2.49595i	−1.87282	+	1.22169i	4.90040			0.828958	−	0.828958i	0.743594	−	0.743594i		−	2.34122i	4.63969	+	0.976259i
373.16	−1.49933	−	1.49933i	1.63420	−	1.63420i			2.49595i	1.87282	−	1.22169i	−4.90040			−0.828958	+	0.828958i	0.743594	−	0.743594i		−	2.34122i	−4.63969	−	0.976259i
373.17	−1.34748	−	1.34748i	−1.68194	+	1.68194i			1.63139i	−1.41767	−	1.72923i	4.53276			−2.13197	+	2.13197i	−0.496689	+	0.496689i		−	2.65785i	−0.419818	+	4.24037i
373.18	−1.34748	−	1.34748i	1.68194	−	1.68194i			1.63139i	1.41767	+	1.72923i	−4.53276			2.13197	−	2.13197i	−0.496689	+	0.496689i		−	2.65785i	0.419818	−	4.24037i
373.19	−1.34183	−	1.34183i	−0.622778	+	0.622778i			1.60103i	−1.44555	+	1.70598i	1.67133			1.38798	−	1.38798i	−0.535345	+	0.535345i			2.22430i	4.22884	−	0.349449i
373.20	−1.34183	−	1.34183i	0.622778	−	0.622778i			1.60103i	1.44555	−	1.70598i	−1.67133			−1.38798	+	1.38798i	−0.535345	+	0.535345i			2.22430i	−4.22884	+	0.349449i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner
11.b	odd	2	1	inner
17.b	even	2	1	inner
55.e	even	4	1	inner
85.g	odd	4	1	inner
187.b	odd	2	1	inner
935.p	even	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	935.2.p.a	✓	208
5.c	odd	4	1	inner	935.2.p.a	✓	208
11.b	odd	2	1	inner	935.2.p.a	✓	208
17.b	even	2	1	inner	935.2.p.a	✓	208
55.e	even	4	1	inner	935.2.p.a	✓	208
85.g	odd	4	1	inner	935.2.p.a	✓	208
187.b	odd	2	1	inner	935.2.p.a	✓	208
935.p	even	4	1	inner	935.2.p.a	✓	208

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
935.2.p.a	✓	208	1.a	even	1	1	trivial
935.2.p.a	✓	208	5.c	odd	4	1	inner
935.2.p.a	✓	208	11.b	odd	2	1	inner
935.2.p.a	✓	208	17.b	even	2	1	inner
935.2.p.a	✓	208	55.e	even	4	1	inner
935.2.p.a	✓	208	85.g	odd	4	1	inner
935.2.p.a	✓	208	187.b	odd	2	1	inner
935.2.p.a	✓	208	935.p	even	4	1	inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(935, [\chi])\).