Newform orbit 175.5.i.e

• Label: 175.5.i.e
• Level: $175$
• Weight: $5$
• Character orbit: 175.i
• Analytic conductor: $18.090$
• Analytic rank: $0$
• Dimension: $28$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	175.i (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(18.0897435397\)
Analytic rank:	\(0\)
Dimension:	\(28\)
Relative dimension:	\(14\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 35)
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.

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

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
26.1	−3.81786	+	6.61273i	1.22175	−	0.705380i	−21.1521	−	36.6365i		0				10.7722i	23.0505	−	43.2397i	200.851			−39.5049	+	68.4245i		0
26.2	−2.99231	+	5.18283i	−2.99712	+	1.73039i	−9.90784	−	17.1609i		0			−	20.7114i	−45.3587	+	18.5361i	22.8354			−34.5115	+	59.7757i		0
26.3	−2.48116	+	4.29750i	8.67875	−	5.01068i	−4.31236	−	7.46922i		0				49.7293i	36.5967	+	32.5834i	−36.5986			9.71376	−	16.8247i		0
26.4	−2.32728	+	4.03096i	−13.6269	+	7.86751i	−2.83245	−	4.90594i		0			−	73.2395i	−19.0150	+	45.1600i	−48.1053			83.2953	−	144.272i		0
26.5	−1.75038	+	3.03175i	13.4663	−	7.77475i	1.87234	+	3.24299i		0				54.4351i	−32.0727	−	37.0452i	−69.1214			80.3936	−	139.246i		0
26.6	−1.21377	+	2.10231i	−6.46725	+	3.73387i	5.05353	+	8.75297i		0			−	18.1282i	43.3169	−	22.9051i	−63.3759			−12.6165	+	21.8524i		0
26.7	−0.332518	+	0.575938i	−3.72093	+	2.14828i	7.77886	+	13.4734i		0			−	2.85737i	−12.8202	−	47.2932i	−20.9870			−31.2698	+	54.1608i		0
26.8	0.332518	−	0.575938i	3.72093	−	2.14828i	7.77886	+	13.4734i		0			−	2.85737i	12.8202	+	47.2932i	20.9870			−31.2698	+	54.1608i		0
26.9	1.21377	−	2.10231i	6.46725	−	3.73387i	5.05353	+	8.75297i		0			−	18.1282i	−43.3169	+	22.9051i	63.3759			−12.6165	+	21.8524i		0
26.10	1.75038	−	3.03175i	−13.4663	+	7.77475i	1.87234	+	3.24299i		0				54.4351i	32.0727	+	37.0452i	69.1214			80.3936	−	139.246i		0
26.11	2.32728	−	4.03096i	13.6269	−	7.86751i	−2.83245	−	4.90594i		0			−	73.2395i	19.0150	−	45.1600i	48.1053			83.2953	−	144.272i		0
26.12	2.48116	−	4.29750i	−8.67875	+	5.01068i	−4.31236	−	7.46922i		0				49.7293i	−36.5967	−	32.5834i	36.5986			9.71376	−	16.8247i		0
26.13	2.99231	−	5.18283i	2.99712	−	1.73039i	−9.90784	−	17.1609i		0			−	20.7114i	45.3587	−	18.5361i	−22.8354			−34.5115	+	59.7757i		0
26.14	3.81786	−	6.61273i	−1.22175	+	0.705380i	−21.1521	−	36.6365i		0				10.7722i	−23.0505	+	43.2397i	−200.851			−39.5049	+	68.4245i		0
101.1	−3.81786	−	6.61273i	1.22175	+	0.705380i	−21.1521	+	36.6365i		0			−	10.7722i	23.0505	+	43.2397i	200.851			−39.5049	−	68.4245i		0
101.2	−2.99231	−	5.18283i	−2.99712	−	1.73039i	−9.90784	+	17.1609i		0				20.7114i	−45.3587	−	18.5361i	22.8354			−34.5115	−	59.7757i		0
101.3	−2.48116	−	4.29750i	8.67875	+	5.01068i	−4.31236	+	7.46922i		0			−	49.7293i	36.5967	−	32.5834i	−36.5986			9.71376	+	16.8247i		0
101.4	−2.32728	−	4.03096i	−13.6269	−	7.86751i	−2.83245	+	4.90594i		0				73.2395i	−19.0150	−	45.1600i	−48.1053			83.2953	+	144.272i		0
101.5	−1.75038	−	3.03175i	13.4663	+	7.77475i	1.87234	−	3.24299i		0			−	54.4351i	−32.0727	+	37.0452i	−69.1214			80.3936	+	139.246i		0
101.6	−1.21377	−	2.10231i	−6.46725	−	3.73387i	5.05353	−	8.75297i		0				18.1282i	43.3169	+	22.9051i	−63.3759			−12.6165	−	21.8524i		0

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	175.5.i.e		28
5.b	even	2	1	inner	175.5.i.e		28
5.c	odd	4	2		35.5.i.a	✓	28
7.d	odd	6	1	inner	175.5.i.e		28
35.i	odd	6	1	inner	175.5.i.e		28
35.k	even	12	2		35.5.i.a	✓	28
35.k	even	12	2		245.5.c.a		28
35.l	odd	12	2		245.5.c.a		28

    

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^28 + 159*T2^26 + 15612*T2^24 + 961557*T2^22 + 43303356*T2^20 + 1414432935*T2^18 + 35245657089*T2^16 + 651643595568*T2^14 + 9120576418632*T2^12 + 90426851538768*T2^10 + 645490916217648*T2^8 + 2764777348349568*T2^6 + 7688442178590336*T2^4 + 3348003005303040*T2^2 + 1266178924894464