Newform orbit 525.3.s.i

• Label: 525.3.s.i
• 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:	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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 26 q^{4} - 36 q^{9}+O(q^{10}) \)

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	−3.36446	−	1.94247i	0.866025	+	1.50000i	5.54641	+	9.60667i		0			−	6.72893i	−3.74107	+	5.91645i		−	27.5553i	−1.50000	+	2.59808i		0
124.2	−2.76065	−	1.59386i	−0.866025	−	1.50000i	3.08079	+	5.33609i		0				5.52130i	3.52639	−	6.04686i		−	6.89053i	−1.50000	+	2.59808i		0
124.3	−2.18474	−	1.26136i	0.866025	+	1.50000i	1.18206	+	2.04738i		0			−	4.36948i	5.96660	−	3.66055i			4.12688i	−1.50000	+	2.59808i		0
124.4	−1.94396	−	1.12234i	−0.866025	−	1.50000i	0.519314	+	0.899478i		0				3.88791i	−0.429379	+	6.98682i			6.64736i	−1.50000	+	2.59808i		0
124.5	−0.369116	−	0.213109i	0.866025	+	1.50000i	−1.90917	−	3.30678i		0			−	0.738232i	−5.30375	−	4.56839i			3.33232i	−1.50000	+	2.59808i		0
124.6	−0.347687	−	0.200737i	−0.866025	−	1.50000i	−1.91941	−	3.32451i		0				0.695374i	−1.84511	−	6.75245i			3.14709i	−1.50000	+	2.59808i		0
124.7	0.347687	+	0.200737i	0.866025	+	1.50000i	−1.91941	−	3.32451i		0				0.695374i	1.84511	+	6.75245i		−	3.14709i	−1.50000	+	2.59808i		0
124.8	0.369116	+	0.213109i	−0.866025	−	1.50000i	−1.90917	−	3.30678i		0			−	0.738232i	5.30375	+	4.56839i		−	3.33232i	−1.50000	+	2.59808i		0
124.9	1.94396	+	1.12234i	0.866025	+	1.50000i	0.519314	+	0.899478i		0				3.88791i	0.429379	−	6.98682i		−	6.64736i	−1.50000	+	2.59808i		0
124.10	2.18474	+	1.26136i	−0.866025	−	1.50000i	1.18206	+	2.04738i		0			−	4.36948i	−5.96660	+	3.66055i		−	4.12688i	−1.50000	+	2.59808i		0
124.11	2.76065	+	1.59386i	0.866025	+	1.50000i	3.08079	+	5.33609i		0				5.52130i	−3.52639	+	6.04686i			6.89053i	−1.50000	+	2.59808i		0
124.12	3.36446	+	1.94247i	−0.866025	−	1.50000i	5.54641	+	9.60667i		0			−	6.72893i	3.74107	−	5.91645i			27.5553i	−1.50000	+	2.59808i		0
199.1	−3.36446	+	1.94247i	0.866025	−	1.50000i	5.54641	−	9.60667i		0				6.72893i	−3.74107	−	5.91645i			27.5553i	−1.50000	−	2.59808i		0
199.2	−2.76065	+	1.59386i	−0.866025	+	1.50000i	3.08079	−	5.33609i		0			−	5.52130i	3.52639	+	6.04686i			6.89053i	−1.50000	−	2.59808i		0
199.3	−2.18474	+	1.26136i	0.866025	−	1.50000i	1.18206	−	2.04738i		0				4.36948i	5.96660	+	3.66055i		−	4.12688i	−1.50000	−	2.59808i		0
199.4	−1.94396	+	1.12234i	−0.866025	+	1.50000i	0.519314	−	0.899478i		0			−	3.88791i	−0.429379	−	6.98682i		−	6.64736i	−1.50000	−	2.59808i		0
199.5	−0.369116	+	0.213109i	0.866025	−	1.50000i	−1.90917	+	3.30678i		0				0.738232i	−5.30375	+	4.56839i		−	3.33232i	−1.50000	−	2.59808i		0
199.6	−0.347687	+	0.200737i	−0.866025	+	1.50000i	−1.91941	+	3.32451i		0			−	0.695374i	−1.84511	+	6.75245i		−	3.14709i	−1.50000	−	2.59808i		0
199.7	0.347687	−	0.200737i	0.866025	−	1.50000i	−1.91941	+	3.32451i		0			−	0.695374i	1.84511	−	6.75245i			3.14709i	−1.50000	−	2.59808i		0
199.8	0.369116	−	0.213109i	−0.866025	+	1.50000i	−1.90917	+	3.30678i		0				0.738232i	5.30375	−	4.56839i			3.33232i	−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.i		24
5.b	even	2	1	inner	525.3.s.i		24
5.c	odd	4	1		525.3.o.n	✓	12
5.c	odd	4	1		525.3.o.o	yes	12
7.d	odd	6	1	inner	525.3.s.i		24
35.i	odd	6	1	inner	525.3.s.i		24
35.k	even	12	1		525.3.o.n	✓	12
35.k	even	12	1		525.3.o.o	yes	12

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
525.3.o.n	✓	12	5.c	odd	4	1
525.3.o.n	✓	12	35.k	even	12	1
525.3.o.o	yes	12	5.c	odd	4	1
525.3.o.o	yes	12	35.k	even	12	1
525.3.s.i		24	1.a	even	1	1	trivial
525.3.s.i		24	5.b	even	2	1	inner
525.3.s.i		24	7.d	odd	6	1	inner
525.3.s.i		24	35.i	odd	6	1	inner

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 - 37*T2^22 + 883*T2^20 - 12538*T2^18 + 129673*T2^16 - 894787*T2^14 + 4521241*T2^12 - 14105734*T2^10 + 28881055*T2^8 - 9445713*T2^6 + 2264625*T2^4 - 253584*T2^2 + 20736

T11^12 + 4*T11^11 + 568*T11^10 + 1384*T11^9 + 224680*T11^8 + 470848*T11^7 + 44114512*T11^6 + 25832032*T11^5 + 6117905344*T11^4 + 3697854720*T11^3 + 316604444160*T11^2 - 579309926400*T11 + 10697609318400

T13^12 - 921*T13^10 + 290211*T13^8 - 38720907*T13^6 + 2416609224*T13^4 - 70140450096*T13^2 + 765779007744