Newform orbit 525.3.s.j

• Label: 525.3.s.j
• Level: $525$
• Weight: $3$
• Character orbit: 525.s
• Analytic conductor: $14.305$
• Analytic rank: $0$
• Dimension: $24$
• CM: no
• Inner twists: $4$

Newspace parameters

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	\(14.3052138789\)
Analytic rank:	\(0\)
Dimension:	\(24\)
Relative dimension:	\(12\) over \(\Q(\zeta_{6})\)
Twist minimal:	no (minimal twist has level 105)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 44 q^{4} - 36 q^{9}+O(q^{10}) \)

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	\( a_{2} \)			\( a_{3} \)			\( a_{4} \)			\( a_{5} \)			\( a_{6} \)			\( a_{7} \)			\( a_{8} \)			\( a_{9} \)			\( a_{10} \)
124.1	−3.44796	−	1.99068i	−0.866025	−	1.50000i	5.92561	+	10.2635i		0				6.89592i	6.61672	+	2.28451i		−	31.2586i	−1.50000	+	2.59808i		0
124.2	−3.12287	−	1.80299i	0.866025	+	1.50000i	4.50153	+	7.79688i		0			−	6.24573i	6.55404	−	2.45857i		−	18.0409i	−1.50000	+	2.59808i		0
124.3	−2.54146	−	1.46731i	0.866025	+	1.50000i	2.30602	+	3.99415i		0			−	5.08293i	−4.43411	+	5.41652i		−	1.79613i	−1.50000	+	2.59808i		0
124.4	−2.17524	−	1.25588i	−0.866025	−	1.50000i	1.15446	+	1.99958i		0				4.35049i	−1.85004	+	6.75110i			4.24760i	−1.50000	+	2.59808i		0
124.5	−1.19112	−	0.687692i	0.866025	+	1.50000i	−1.05416	−	1.82586i		0			−	2.38224i	−2.42539	−	6.56639i			8.40129i	−1.50000	+	2.59808i		0
124.6	−0.499806	−	0.288563i	0.866025	+	1.50000i	−1.83346	−	3.17565i		0			−	0.999611i	6.80420	+	1.64406i			4.42478i	−1.50000	+	2.59808i		0
124.7	0.499806	+	0.288563i	−0.866025	−	1.50000i	−1.83346	−	3.17565i		0			−	0.999611i	−6.80420	−	1.64406i		−	4.42478i	−1.50000	+	2.59808i		0
124.8	1.19112	+	0.687692i	−0.866025	−	1.50000i	−1.05416	−	1.82586i		0			−	2.38224i	2.42539	+	6.56639i		−	8.40129i	−1.50000	+	2.59808i		0
124.9	2.17524	+	1.25588i	0.866025	+	1.50000i	1.15446	+	1.99958i		0				4.35049i	1.85004	−	6.75110i		−	4.24760i	−1.50000	+	2.59808i		0
124.10	2.54146	+	1.46731i	−0.866025	−	1.50000i	2.30602	+	3.99415i		0			−	5.08293i	4.43411	−	5.41652i			1.79613i	−1.50000	+	2.59808i		0
124.11	3.12287	+	1.80299i	−0.866025	−	1.50000i	4.50153	+	7.79688i		0			−	6.24573i	−6.55404	+	2.45857i			18.0409i	−1.50000	+	2.59808i		0
124.12	3.44796	+	1.99068i	0.866025	+	1.50000i	5.92561	+	10.2635i		0				6.89592i	−6.61672	−	2.28451i			31.2586i	−1.50000	+	2.59808i		0
199.1	−3.44796	+	1.99068i	−0.866025	+	1.50000i	5.92561	−	10.2635i		0			−	6.89592i	6.61672	−	2.28451i			31.2586i	−1.50000	−	2.59808i		0
199.2	−3.12287	+	1.80299i	0.866025	−	1.50000i	4.50153	−	7.79688i		0				6.24573i	6.55404	+	2.45857i			18.0409i	−1.50000	−	2.59808i		0
199.3	−2.54146	+	1.46731i	0.866025	−	1.50000i	2.30602	−	3.99415i		0				5.08293i	−4.43411	−	5.41652i			1.79613i	−1.50000	−	2.59808i		0
199.4	−2.17524	+	1.25588i	−0.866025	+	1.50000i	1.15446	−	1.99958i		0			−	4.35049i	−1.85004	−	6.75110i		−	4.24760i	−1.50000	−	2.59808i		0
199.5	−1.19112	+	0.687692i	0.866025	−	1.50000i	−1.05416	+	1.82586i		0				2.38224i	−2.42539	+	6.56639i		−	8.40129i	−1.50000	−	2.59808i		0
199.6	−0.499806	+	0.288563i	0.866025	−	1.50000i	−1.83346	+	3.17565i		0				0.999611i	6.80420	−	1.64406i		−	4.42478i	−1.50000	−	2.59808i		0
199.7	0.499806	−	0.288563i	−0.866025	+	1.50000i	−1.83346	+	3.17565i		0				0.999611i	−6.80420	+	1.64406i			4.42478i	−1.50000	−	2.59808i		0
199.8	1.19112	−	0.687692i	−0.866025	+	1.50000i	−1.05416	+	1.82586i		0				2.38224i	2.42539	−	6.56639i			8.40129i	−1.50000	−	2.59808i		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	525.3.s.j		24
5.b	even	2	1	inner	525.3.s.j		24
5.c	odd	4	1		105.3.n.b	✓	12
5.c	odd	4	1		525.3.o.m		12
7.d	odd	6	1	inner	525.3.s.j		24
15.e	even	4	1		315.3.w.b		12
35.i	odd	6	1	inner	525.3.s.j		24
35.k	even	12	1		105.3.n.b	✓	12
35.k	even	12	1		525.3.o.m		12
35.k	even	12	1		735.3.h.b		12
35.l	odd	12	1		735.3.h.b		12
105.w	odd	12	1		315.3.w.b		12

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
105.3.n.b	✓	12	5.c	odd	4	1
105.3.n.b	✓	12	35.k	even	12	1
315.3.w.b		12	15.e	even	4	1
315.3.w.b		12	105.w	odd	12	1
525.3.o.m		12	5.c	odd	4	1
525.3.o.m		12	35.k	even	12	1
525.3.s.j		24	1.a	even	1	1	trivial
525.3.s.j		24	5.b	even	2	1	inner
525.3.s.j		24	7.d	odd	6	1	inner
525.3.s.j		24	35.i	odd	6	1	inner
735.3.h.b		12	35.k	even	12	1
735.3.h.b		12	35.l	odd	12	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{3}^{\mathrm{new}}(525, [\chi])\):

T2^24 - 46*T2^22 + 1327*T2^20 - 23878*T2^18 + 314989*T2^16 - 2905264*T2^14 + 19943140*T2^12 - 92745568*T2^10 + 304019392*T2^8 - 523870464*T2^6 + 620087616*T2^4 - 196439040*T2^2 + 49787136

T11^12 - 20*T11^11 + 649*T11^10 - 1808*T11^9 + 99307*T11^8 + 399706*T11^7 + 19317370*T11^6 + 117168772*T11^5 + 829250704*T11^4 + 1522820856*T11^3 + 4327265688*T11^2 - 2751516432*T11 + 15854839056

T13^12 - 978*T13^10 + 326655*T13^8 - 49084380*T13^6 + 3468233295*T13^4 - 102432549618*T13^2 + 732611029329