Newform orbit 35.5.g.a

• Label: 35.5.g.a
• Level: $35$
• Weight: $5$
• Character orbit: 35.g
• Analytic conductor: $3.618$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.g (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.61794870793\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
8.1	−5.44757	+	5.44757i	1.36639	+	1.36639i		−	43.3520i	7.20796	−	23.9384i	−14.8870			−13.0958	+	13.0958i	149.002	+	149.002i		−	77.2660i	91.1401	+	169.672i
8.2	−4.43769	+	4.43769i	−10.8098	−	10.8098i		−	23.3862i	8.86080	+	23.3770i	95.9409			13.0958	−	13.0958i	32.7776	+	32.7776i			152.703i	−143.062	−	64.4186i
8.3	−3.63546	+	3.63546i	2.99367	+	2.99367i		−	10.4331i	−2.80777	+	24.8418i	−21.7667			−13.0958	+	13.0958i	−20.2382	−	20.2382i		−	63.0758i	−80.1039	−	100.519i
8.4	−2.97419	+	2.97419i	−1.22954	−	1.22954i		−	1.69164i	−22.1755	−	11.5432i	7.31376			13.0958	−	13.0958i	−42.5558	−	42.5558i		−	77.9765i	100.286	−	31.6225i
8.5	−2.88957	+	2.88957i	11.3498	+	11.3498i		−	0.699277i	24.2963	−	5.88989i	−65.5923			13.0958	−	13.0958i	−44.2126	−	44.2126i			176.637i	−53.1866	+	87.2252i
8.6	−0.0151985	+	0.0151985i	8.40408	+	8.40408i			15.9995i	−24.2998	−	5.87527i	−0.255459			−13.0958	+	13.0958i	−0.486345	−	0.486345i			60.2572i	0.458616	−	0.280025i
8.7	0.896879	−	0.896879i	−9.60523	−	9.60523i			14.3912i	−20.2649	+	14.6401i	−17.2295			−13.0958	+	13.0958i	27.2572	+	27.2572i			103.521i	−5.04483	+	31.3056i
8.8	1.48373	−	1.48373i	2.63880	+	2.63880i			11.5971i	8.51221	+	23.5062i	7.83054			13.0958	−	13.0958i	40.9466	+	40.9466i		−	67.0734i	47.5067	+	22.2471i
8.9	3.18640	−	3.18640i	5.77081	+	5.77081i		−	4.30624i	16.7353	−	18.5723i	36.7762			−13.0958	+	13.0958i	37.2610	+	37.2610i		−	14.3955i	−5.85321	−	112.504i
8.10	3.68989	−	3.68989i	−5.41571	−	5.41571i		−	11.2306i	−14.8082	−	20.1424i	−39.9667			13.0958	−	13.0958i	17.5987	+	17.5987i		−	22.3403i	−128.964	−	19.6826i
8.11	5.01495	−	5.01495i	−5.80055	−	5.80055i		−	34.2994i	17.0417	+	18.2915i	−58.1789			−13.0958	+	13.0958i	−91.7707	−	91.7707i		−	13.7072i	177.194	+	6.26750i
8.12	5.12784	−	5.12784i	10.3372	+	10.3372i		−	36.5894i	−22.2980	+	11.3048i	106.015			13.0958	−	13.0958i	−105.579	−	105.579i			132.716i	−56.3718	+	172.310i
22.1	−5.44757	−	5.44757i	1.36639	−	1.36639i			43.3520i	7.20796	+	23.9384i	−14.8870			−13.0958	−	13.0958i	149.002	−	149.002i			77.2660i	91.1401	−	169.672i
22.2	−4.43769	−	4.43769i	−10.8098	+	10.8098i			23.3862i	8.86080	−	23.3770i	95.9409			13.0958	+	13.0958i	32.7776	−	32.7776i		−	152.703i	−143.062	+	64.4186i
22.3	−3.63546	−	3.63546i	2.99367	−	2.99367i			10.4331i	−2.80777	−	24.8418i	−21.7667			−13.0958	−	13.0958i	−20.2382	+	20.2382i			63.0758i	−80.1039	+	100.519i
22.4	−2.97419	−	2.97419i	−1.22954	+	1.22954i			1.69164i	−22.1755	+	11.5432i	7.31376			13.0958	+	13.0958i	−42.5558	+	42.5558i			77.9765i	100.286	+	31.6225i
22.5	−2.88957	−	2.88957i	11.3498	−	11.3498i			0.699277i	24.2963	+	5.88989i	−65.5923			13.0958	+	13.0958i	−44.2126	+	44.2126i		−	176.637i	−53.1866	−	87.2252i
22.6	−0.0151985	−	0.0151985i	8.40408	−	8.40408i		−	15.9995i	−24.2998	+	5.87527i	−0.255459			−13.0958	−	13.0958i	−0.486345	+	0.486345i		−	60.2572i	0.458616	+	0.280025i
22.7	0.896879	+	0.896879i	−9.60523	+	9.60523i		−	14.3912i	−20.2649	−	14.6401i	−17.2295			−13.0958	−	13.0958i	27.2572	−	27.2572i		−	103.521i	−5.04483	−	31.3056i
22.8	1.48373	+	1.48373i	2.63880	−	2.63880i		−	11.5971i	8.51221	−	23.5062i	7.83054			13.0958	+	13.0958i	40.9466	−	40.9466i			67.0734i	47.5067	−	22.2471i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.c	odd	4	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	35.5.g.a	✓	24
5.b	even	2	1		175.5.g.c		24
5.c	odd	4	1	inner	35.5.g.a	✓	24
5.c	odd	4	1		175.5.g.c		24

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
35.5.g.a	✓	24	1.a	even	1	1	trivial
35.5.g.a	✓	24	5.c	odd	4	1	inner
175.5.g.c		24	5.b	even	2	1
175.5.g.c		24	5.c	odd	4	1

Hecke kernels

This newform subspace is the entire newspace \(S_{5}^{\mathrm{new}}(35, [\chi])\).