Newform orbit 175.5.c.d

• Label: 175.5.c.d
• Level: $175$
• Weight: $5$
• Character orbit: 175.c
• Analytic conductor: $18.090$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	175.c (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(18.0897435397\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Twist minimal:	no (minimal twist has level 35)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 244 q^{4} + 868 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
174.1		−	4.81769i	14.5704			−7.21016				0			−	70.1957i	−19.6236	−	44.8989i		−	42.3467i	131.296				0
174.2			4.81769i	14.5704			−7.21016				0				70.1957i	−19.6236	+	44.8989i			42.3467i	131.296				0
174.3		−	3.23331i	14.6970			5.54568				0			−	47.5200i	41.0994	−	26.6804i		−	69.6640i	135.002				0
174.4			3.23331i	14.6970			5.54568				0				47.5200i	41.0994	+	26.6804i			69.6640i	135.002				0
174.5		−	7.63119i	12.6955			−42.2350				0			−	96.8817i	−48.9579	+	2.03056i			200.204i	80.1757				0
174.6			7.63119i	12.6955			−42.2350				0				96.8817i	−48.9579	−	2.03056i		−	200.204i	80.1757				0
174.7		−	6.50299i	5.52807			−26.2889				0			−	35.9490i	44.7373	+	19.9894i			66.9085i	−50.4404				0
174.8			6.50299i	5.52807			−26.2889				0				35.9490i	44.7373	−	19.9894i		−	66.9085i	−50.4404				0
174.9		−	1.17355i	−9.10378			14.6228				0				10.6837i	27.5814	+	40.5002i		−	35.9373i	1.87877				0
174.10			1.17355i	−9.10378			14.6228				0			−	10.6837i	27.5814	−	40.5002i			35.9373i	1.87877				0
174.11		−	4.62973i	−0.296012			−5.43443				0				1.37046i	46.5696	+	15.2405i		−	48.9158i	−80.9124				0
174.12			4.62973i	−0.296012			−5.43443				0			−	1.37046i	46.5696	−	15.2405i			48.9158i	−80.9124				0
174.13		−	4.62973i	0.296012			−5.43443				0			−	1.37046i	−46.5696	+	15.2405i		−	48.9158i	−80.9124				0
174.14			4.62973i	0.296012			−5.43443				0				1.37046i	−46.5696	−	15.2405i			48.9158i	−80.9124				0
174.15		−	1.17355i	9.10378			14.6228				0			−	10.6837i	−27.5814	+	40.5002i		−	35.9373i	1.87877				0
174.16			1.17355i	9.10378			14.6228				0				10.6837i	−27.5814	−	40.5002i			35.9373i	1.87877				0
174.17		−	6.50299i	−5.52807			−26.2889				0				35.9490i	−44.7373	+	19.9894i			66.9085i	−50.4404				0
174.18			6.50299i	−5.52807			−26.2889				0			−	35.9490i	−44.7373	−	19.9894i		−	66.9085i	−50.4404				0
174.19		−	7.63119i	−12.6955			−42.2350				0				96.8817i	48.9579	+	2.03056i			200.204i	80.1757				0
174.20			7.63119i	−12.6955			−42.2350				0			−	96.8817i	48.9579	−	2.03056i		−	200.204i	80.1757				0

Inner twists

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

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	175.5.c.d		24
5.b	even	2	1	inner	175.5.c.d		24
5.c	odd	4	1		35.5.d.a	✓	12
5.c	odd	4	1		175.5.d.i		12
7.b	odd	2	1	inner	175.5.c.d		24
15.e	even	4	1		315.5.h.a		12
20.e	even	4	1		560.5.f.b		12
35.c	odd	2	1	inner	175.5.c.d		24
35.f	even	4	1		35.5.d.a	✓	12
35.f	even	4	1		175.5.d.i		12
105.k	odd	4	1		315.5.h.a		12
140.j	odd	4	1		560.5.f.b		12

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
35.5.d.a	✓	12	5.c	odd	4	1
35.5.d.a	✓	12	35.f	even	4	1
175.5.c.d		24	1.a	even	1	1	trivial
175.5.c.d		24	5.b	even	2	1	inner
175.5.c.d		24	7.b	odd	2	1	inner
175.5.c.d		24	35.c	odd	2	1	inner
175.5.d.i		12	5.c	odd	4	1
175.5.d.i		12	35.f	even	4	1
315.5.h.a		12	15.e	even	4	1
315.5.h.a		12	105.k	odd	4	1
560.5.f.b		12	20.e	even	4	1
560.5.f.b		12	140.j	odd	4	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{12} + 157T_{2}^{10} + 9180T_{2}^{8} + 250168T_{2}^{6} + 3224944T_{2}^{4} + 16798800T_{2}^{2} + 17640000 \) acting on \(S_{5}^{\mathrm{new}}(175, [\chi])\).