Newform orbit 935.2.e.a

• Label: 935.2.e.a
• Level: $935$
• Weight: $2$
• Character orbit: 935.e
• Analytic conductor: $7.466$
• Analytic rank: $0$
• Dimension: $88$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 935 = 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	935.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(7.46601258899\)
Analytic rank:	\(0\)
Dimension:	\(88\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 88 q - 76 q^{4} + 80 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
254.1		−	2.78933i	−1.40318			−5.78037			−1.54610	−	1.61542i			3.91392i	2.62976					10.5447i	−1.03110			−4.50595	+	4.31257i
254.2		−	2.78933i	1.40318			−5.78037			1.54610	+	1.61542i		−	3.91392i	−2.62976					10.5447i	−1.03110			4.50595	−	4.31257i
254.3		−	2.59422i	−2.19606			−4.72996			1.06355	+	1.96694i			5.69704i	2.42078					7.08211i	1.82266			5.10268	−	2.75908i
254.4		−	2.59422i	2.19606			−4.72996			−1.06355	−	1.96694i		−	5.69704i	−2.42078					7.08211i	1.82266			−5.10268	+	2.75908i
254.5		−	2.53473i	−1.14542			−4.42483			−1.27554	+	1.83657i			2.90333i	−4.98299					6.14628i	−1.68801			4.65520	+	3.23315i
254.6		−	2.53473i	1.14542			−4.42483			1.27554	−	1.83657i		−	2.90333i	4.98299					6.14628i	−1.68801			−4.65520	−	3.23315i
254.7		−	2.32464i	−0.0254138			−3.40395			2.01305	−	0.973460i			0.0590779i	−1.34192					3.26368i	−2.99935			−2.26294	−	4.67962i
254.8		−	2.32464i	0.0254138			−3.40395			−2.01305	+	0.973460i		−	0.0590779i	1.34192					3.26368i	−2.99935			2.26294	+	4.67962i
254.9		−	2.27567i	−2.76186			−3.17867			−0.589974	−	2.15683i			6.28507i	−2.31007					2.68226i	4.62786			−4.90824	+	1.34259i
254.10		−	2.27567i	2.76186			−3.17867			0.589974	+	2.15683i		−	6.28507i	2.31007					2.68226i	4.62786			4.90824	−	1.34259i
254.11		−	2.17409i	−0.485029			−2.72665			−0.603941	+	2.15296i			1.05450i	2.68547					1.57981i	−2.76475			4.68073	+	1.31302i
254.12		−	2.17409i	0.485029			−2.72665			0.603941	−	2.15296i		−	1.05450i	−2.68547					1.57981i	−2.76475			−4.68073	−	1.31302i
254.13		−	2.08814i	−3.01273			−2.36033			−2.21636	+	0.296201i			6.29099i	3.53808					0.752410i	6.07653			0.618510	+	4.62807i
254.14		−	2.08814i	3.01273			−2.36033			2.21636	−	0.296201i		−	6.29099i	−3.53808					0.752410i	6.07653			−0.618510	−	4.62807i
254.15		−	2.04389i	−0.841119			−2.17747			−1.66399	−	1.49370i			1.71915i	0.492566					0.362735i	−2.29252			−3.05295	+	3.40101i
254.16		−	2.04389i	0.841119			−2.17747			1.66399	+	1.49370i		−	1.71915i	−0.492566					0.362735i	−2.29252			3.05295	−	3.40101i
254.17		−	1.74271i	−3.36243			−1.03705			1.84310	+	1.26609i			5.85976i	−1.59471				−	1.67814i	8.30595			2.20644	−	3.21199i
254.18		−	1.74271i	3.36243			−1.03705			−1.84310	−	1.26609i		−	5.85976i	1.59471				−	1.67814i	8.30595			−2.20644	+	3.21199i
254.19		−	1.67872i	−1.10294			−0.818093			1.39660	+	1.74628i			1.85153i	−3.15053				−	1.98409i	−1.78352			2.93152	−	2.34450i
254.20		−	1.67872i	1.10294			−0.818093			−1.39660	−	1.74628i		−	1.85153i	3.15053				−	1.98409i	−1.78352			−2.93152	+	2.34450i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
17.b	even	2	1	inner
85.c	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	935.2.e.a	✓	88
5.b	even	2	1	inner	935.2.e.a	✓	88
17.b	even	2	1	inner	935.2.e.a	✓	88
85.c	even	2	1	inner	935.2.e.a	✓	88

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
935.2.e.a	✓	88	1.a	even	1	1	trivial
935.2.e.a	✓	88	5.b	even	2	1	inner
935.2.e.a	✓	88	17.b	even	2	1	inner
935.2.e.a	✓	88	85.c	even	2	1	inner

Hecke kernels

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