Newform orbit 175.5.j.b

• Label: 175.5.j.b
• Level: $175$
• Weight: $5$
• Character orbit: 175.j
• Analytic conductor: $18.090$
• Analytic rank: $0$
• Dimension: $40$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	175.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(18.0897435397\)
Analytic rank:	\(0\)
Dimension:	\(40\)
Relative dimension:	\(20\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 40 q + 116 q^{4} - 532 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
24.1	−5.90633	+	3.41002i	4.05479	−	7.02310i	15.2565	−	26.4250i		0				55.3077i	−25.2546	−	41.9906i			98.9794i	7.61740	+	13.1937i		0
24.2	−5.87152	+	3.38992i	−8.34918	+	14.4612i	14.9831	−	25.9515i		0			−	113.212i	6.53743	−	48.5619i			94.6891i	−98.9176	−	171.330i		0
24.3	−5.77068	+	3.33171i	1.39210	−	2.41118i	14.2005	−	24.5960i		0				18.5522i	−48.4605	−	7.25097i			82.6333i	36.6241	+	63.4349i		0
24.4	−5.10266	+	2.94602i	4.33829	−	7.51414i	9.35812	−	16.2087i		0				51.1228i	45.7349	+	17.5876i			16.0042i	2.85850	+	4.95108i		0
24.5	−3.52390	+	2.03453i	7.35058	−	12.7316i	0.278590	−	0.482532i		0				59.8198i	47.6851	+	11.2754i		−	62.8376i	−67.5621	−	117.021i		0
24.6	−3.39498	+	1.96009i	−2.45966	+	4.26025i	−0.316095	+	0.547493i		0			−	19.2846i	−34.3969	−	34.8977i		−	65.2012i	28.4002	+	49.1905i		0
24.7	−2.04601	+	1.18127i	−4.41391	+	7.64511i	−5.20922	+	9.02264i		0			−	20.8560i	48.9708	+	1.69012i		−	62.4144i	1.53484	+	2.65843i		0
24.8	−1.83982	+	1.06222i	1.80571	−	3.12759i	−5.74337	+	9.94782i		0				7.67226i	−12.2893	+	47.4339i		−	58.3940i	33.9788	+	58.8530i		0
24.9	−1.70026	+	0.981645i	6.43269	−	11.1418i	−6.07275	+	10.5183i		0				25.2585i	0.997416	−	48.9898i		−	55.2577i	−42.2591	−	73.1949i		0
24.10	−0.629951	+	0.363703i	−6.15528	+	10.6613i	−7.73544	+	13.3982i		0			−	8.95477i	27.8063	−	40.3461i		−	22.8921i	−35.2750	−	61.0981i		0
24.11	0.629951	−	0.363703i	6.15528	−	10.6613i	−7.73544	+	13.3982i		0			−	8.95477i	−27.8063	+	40.3461i			22.8921i	−35.2750	−	61.0981i		0
24.12	1.70026	−	0.981645i	−6.43269	+	11.1418i	−6.07275	+	10.5183i		0				25.2585i	−0.997416	+	48.9898i			55.2577i	−42.2591	−	73.1949i		0
24.13	1.83982	−	1.06222i	−1.80571	+	3.12759i	−5.74337	+	9.94782i		0				7.67226i	12.2893	−	47.4339i			58.3940i	33.9788	+	58.8530i		0
24.14	2.04601	−	1.18127i	4.41391	−	7.64511i	−5.20922	+	9.02264i		0			−	20.8560i	−48.9708	−	1.69012i			62.4144i	1.53484	+	2.65843i		0
24.15	3.39498	−	1.96009i	2.45966	−	4.26025i	−0.316095	+	0.547493i		0			−	19.2846i	34.3969	+	34.8977i			65.2012i	28.4002	+	49.1905i		0
24.16	3.52390	−	2.03453i	−7.35058	+	12.7316i	0.278590	−	0.482532i		0				59.8198i	−47.6851	−	11.2754i			62.8376i	−67.5621	−	117.021i		0
24.17	5.10266	−	2.94602i	−4.33829	+	7.51414i	9.35812	−	16.2087i		0				51.1228i	−45.7349	−	17.5876i		−	16.0042i	2.85850	+	4.95108i		0
24.18	5.77068	−	3.33171i	−1.39210	+	2.41118i	14.2005	−	24.5960i		0				18.5522i	48.4605	+	7.25097i		−	82.6333i	36.6241	+	63.4349i		0
24.19	5.87152	−	3.38992i	8.34918	−	14.4612i	14.9831	−	25.9515i		0			−	113.212i	−6.53743	+	48.5619i		−	94.6891i	−98.9176	−	171.330i		0
24.20	5.90633	−	3.41002i	−4.05479	+	7.02310i	15.2565	−	26.4250i		0				55.3077i	25.2546	+	41.9906i		−	98.9794i	7.61740	+	13.1937i		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.j.b		40
5.b	even	2	1	inner	175.5.j.b		40
5.c	odd	4	1		35.5.h.a	✓	20
5.c	odd	4	1		175.5.i.b		20
7.d	odd	6	1	inner	175.5.j.b		40
35.i	odd	6	1	inner	175.5.j.b		40
35.k	even	12	1		35.5.h.a	✓	20
35.k	even	12	1		175.5.i.b		20
35.k	even	12	1		245.5.d.a		20
35.l	odd	12	1		245.5.d.a		20

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
35.5.h.a	✓	20	5.c	odd	4	1
35.5.h.a	✓	20	35.k	even	12	1
175.5.i.b		20	5.c	odd	4	1
175.5.i.b		20	35.k	even	12	1
175.5.j.b		40	1.a	even	1	1	trivial
175.5.j.b		40	5.b	even	2	1	inner
175.5.j.b		40	7.d	odd	6	1	inner
175.5.j.b		40	35.i	odd	6	1	inner
245.5.d.a		20	35.k	even	12	1
245.5.d.a		20	35.l	odd	12	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator T2^40 - 218*T2^38 + 27777*T2^36 - 2378230*T2^34 + 152447654*T2^32 - 7504059618*T2^30 + 292158243853*T2^28 - 9005885774234*T2^26 + 221768914924662*T2^24 - 4318033480372286*T2^22 + 66706454557932793*T2^20 - 804099953904132714*T2^18 + 7563354117374923337*T2^16 - 54053793014376696856*T2^14 + 297403175855785868568*T2^12 - 1219683681750839352032*T2^10 + 3732202985813375026096*T2^8 - 7770630838345675306752*T2^6 + 10583887767314585516928*T2^4 - 5141761225040904662016*T2^2 + 1856128870430496297216