Space of modular forms of level 525, weight 3, and Character 525.s

• Label: 525.3.s
• Level: $525$
• Weight: $3$
• Character orbit: 525.s
• Rep. character: $\chi_{525}(124,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $10$
• Sturm bound: $240$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(240\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(2\), \(11\), \(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(525, [\chi])\).

	Total	New	Old
Modular forms	344	96	248
Cusp forms	296	96	200
Eisenstein series	48	0	48

Trace form

\( 96 q + 96 q^{4} - 144 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(525, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
525.3.s.a	$525$	$3$	525.s	35.i	$6$	$4$	$2$	$14.305$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}-3\zeta_{12}^{2}q^{4}+\cdots\)
525.3.s.b	$525$	$3$	525.s	35.i	$6$	$4$	$2$	$14.305$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}-3\zeta_{12}^{2}q^{4}+\cdots\)
525.3.s.c	$525$	$3$	525.s	35.i	$6$	$4$	$2$	$14.305$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}-3\zeta_{12}^{2}q^{4}+\cdots\)
525.3.s.d	$525$	$3$	525.s	35.i	$6$	$4$	$2$	$14.305$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+2\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+(-2+\cdots)q^{6}+\cdots\)
525.3.s.e	$525$	$3$	525.s	35.i	$6$	$4$	$2$	$14.305$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+3\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+5\zeta_{12}^{2}q^{4}+\cdots\)
525.3.s.f	$525$	$3$	525.s	35.i	$6$	$4$	$2$	$14.305$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+3\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+5\zeta_{12}^{2}q^{4}+\cdots\)
525.3.s.g	$525$	$3$	525.s	35.i	$6$	$8$	$4$	$14.305$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\zeta_{24}-\zeta_{24}^{4})q^{2}+(\zeta_{24}+\zeta_{24}^{3})q^{3}+\cdots\)
525.3.s.h	$525$	$3$	525.s	35.i	$6$	$16$	$8$	$14.305$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{11}q^{2}+(-\beta _{10}+2\beta _{13})q^{3}+(1+\cdots)q^{4}+\cdots\)
525.3.s.i	$525$	$3$	525.s	35.i	$6$	$24$	$12$	$14.305$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
525.3.s.j	$525$	$3$	525.s	35.i	$6$	$24$	$12$	$14.305$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)