Newform orbit 35.5.i.a

• Label: 35.5.i.a
• Level: $35$
• Weight: $5$
• Character orbit: 35.i
• Analytic conductor: $3.618$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.i (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(3.61794870793\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(14\) over \(\Q(\zeta_{6})\)
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 94 q^{4} - 30 q^{5} - 222 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
19.1	−6.61273	−	3.81786i	−0.705380	−	1.22175i	21.1521	+	36.6365i	−23.8771	+	7.40838i			10.7722i	43.2397	+	23.0505i		−	200.851i	39.5049	−	68.4245i	186.177	+	42.1698i
19.2	−5.18283	−	2.99231i	1.73039	+	2.99712i	9.90784	+	17.1609i	24.7118	+	3.78477i		−	20.7114i	−18.5361	−	45.3587i		−	22.8354i	34.5115	−	59.7757i	−116.752	−	93.5614i
19.3	−4.29750	−	2.48116i	−5.01068	−	8.67875i	4.31236	+	7.46922i	4.41022	−	24.6079i			49.7293i	−32.5834	+	36.5967i			36.5986i	−9.71376	+	16.8247i	−80.0093	+	94.8102i
19.4	−4.03096	−	2.32728i	7.86751	+	13.6269i	2.83245	+	4.90594i	−24.7840	−	3.27931i		−	73.2395i	−45.1600	−	19.0150i			48.1053i	−83.2953	+	144.272i	92.2715	+	70.8980i
19.5	−3.03175	−	1.75038i	−7.77475	−	13.4663i	−1.87234	−	3.24299i	−2.74588	+	24.8487i			54.4351i	37.0452	−	32.0727i			69.1214i	−80.3936	+	139.246i	51.8195	−	70.5288i
19.6	−2.10231	−	1.21377i	3.73387	+	6.46725i	−5.05353	−	8.75297i	11.6512	+	22.1190i		−	18.1282i	22.9051	+	43.3169i			63.3759i	12.6165	−	21.8524i	2.35294	−	60.6428i
19.7	−0.575938	−	0.332518i	2.14828	+	3.72093i	−7.77886	−	13.4734i	−2.48237	−	24.8765i		−	2.85737i	47.2932	−	12.8202i			20.9870i	31.2698	−	54.1608i	−6.84217	+	15.1527i
19.8	0.575938	+	0.332518i	−2.14828	−	3.72093i	−7.77886	−	13.4734i	−22.7848	+	10.2884i		−	2.85737i	−47.2932	+	12.8202i		−	20.9870i	31.2698	−	54.1608i	−16.5437	−	1.65087i
19.9	2.10231	+	1.21377i	−3.73387	−	6.46725i	−5.05353	−	8.75297i	24.9812	−	0.969268i		−	18.1282i	−22.9051	−	43.3169i		−	63.3759i	12.6165	−	21.8524i	53.6947	+	28.2837i
19.10	3.03175	+	1.75038i	7.77475	+	13.4663i	−1.87234	−	3.24299i	20.1467	−	14.8024i			54.4351i	−37.0452	+	32.0727i		−	69.1214i	−80.3936	+	139.246i	86.9895	−	9.61266i
19.11	4.03096	+	2.32728i	−7.86751	−	13.6269i	2.83245	+	4.90594i	−15.2320	−	19.8239i		−	73.2395i	45.1600	+	19.0150i		−	48.1053i	−83.2953	+	144.272i	−15.2637	−	115.358i
19.12	4.29750	+	2.48116i	5.01068	+	8.67875i	4.31236	+	7.46922i	−19.1060	+	16.1233i			49.7293i	32.5834	−	36.5967i		−	36.5986i	−9.71376	+	16.8247i	−122.113	+	21.8850i
19.13	5.18283	+	2.99231i	−1.73039	−	2.99712i	9.90784	+	17.1609i	15.6336	+	19.5087i		−	20.7114i	18.5361	+	45.3587i			22.8354i	34.5115	−	59.7757i	22.6504	+	147.891i
19.14	6.61273	+	3.81786i	0.705380	+	1.22175i	21.1521	+	36.6365i	−5.52270	−	24.3824i			10.7722i	−43.2397	−	23.0505i			200.851i	39.5049	−	68.4245i	56.5683	−	182.319i
24.1	−6.61273	+	3.81786i	−0.705380	+	1.22175i	21.1521	−	36.6365i	−23.8771	−	7.40838i		−	10.7722i	43.2397	−	23.0505i			200.851i	39.5049	+	68.4245i	186.177	−	42.1698i
24.2	−5.18283	+	2.99231i	1.73039	−	2.99712i	9.90784	−	17.1609i	24.7118	−	3.78477i			20.7114i	−18.5361	+	45.3587i			22.8354i	34.5115	+	59.7757i	−116.752	+	93.5614i
24.3	−4.29750	+	2.48116i	−5.01068	+	8.67875i	4.31236	−	7.46922i	4.41022	+	24.6079i		−	49.7293i	−32.5834	−	36.5967i		−	36.5986i	−9.71376	−	16.8247i	−80.0093	−	94.8102i
24.4	−4.03096	+	2.32728i	7.86751	−	13.6269i	2.83245	−	4.90594i	−24.7840	+	3.27931i			73.2395i	−45.1600	+	19.0150i		−	48.1053i	−83.2953	−	144.272i	92.2715	−	70.8980i
24.5	−3.03175	+	1.75038i	−7.77475	+	13.4663i	−1.87234	+	3.24299i	−2.74588	−	24.8487i		−	54.4351i	37.0452	+	32.0727i		−	69.1214i	−80.3936	−	139.246i	51.8195	+	70.5288i
24.6	−2.10231	+	1.21377i	3.73387	−	6.46725i	−5.05353	+	8.75297i	11.6512	−	22.1190i			18.1282i	22.9051	−	43.3169i		−	63.3759i	12.6165	+	21.8524i	2.35294	+	60.6428i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner
7.d	odd	6	1	inner
35.i	odd	6	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	35.5.i.a	✓	28
5.b	even	2	1	inner	35.5.i.a	✓	28
5.c	odd	4	2		175.5.i.e		28
7.c	even	3	1		245.5.c.a		28
7.d	odd	6	1	inner	35.5.i.a	✓	28
7.d	odd	6	1		245.5.c.a		28
35.i	odd	6	1	inner	35.5.i.a	✓	28
35.i	odd	6	1		245.5.c.a		28
35.j	even	6	1		245.5.c.a		28
35.k	even	12	2		175.5.i.e		28

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
35.5.i.a	✓	28	1.a	even	1	1	trivial
35.5.i.a	✓	28	5.b	even	2	1	inner
35.5.i.a	✓	28	7.d	odd	6	1	inner
35.5.i.a	✓	28	35.i	odd	6	1	inner
175.5.i.e		28	5.c	odd	4	2
175.5.i.e		28	35.k	even	12	2
245.5.c.a		28	7.c	even	3	1
245.5.c.a		28	7.d	odd	6	1
245.5.c.a		28	35.i	odd	6	1
245.5.c.a		28	35.j	even	6	1

Hecke kernels

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