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

• Label: 525.3.l
• Level: $525$
• Weight: $3$
• Character orbit: 525.l
• Rep. character: $\chi_{525}(43,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $72$
• Newform subspaces: $5$
• Sturm bound: $240$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.l (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(240\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	344	72	272
Cusp forms	296	72	224
Eisenstein series	48	0	48

Trace form

\( 72 q - 8 q^{2} - 48 q^{6} + 48 q^{8} + O(q^{10}) \)

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.l.a	$525$	$3$	525.l	5.c	$4$	$8$	$4$	$14.305$	8.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+(\beta _{5}+\beta _{7})q^{3}+(-\beta _{4}+\beta _{6}+\cdots)q^{4}+\cdots\)
525.3.l.b	$525$	$3$	525.l	5.c	$4$	$8$	$4$	$14.305$	8.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{2}q^{2}-\beta _{6}q^{3}+3\beta _{3}q^{4}-\beta _{4}q^{6}+\cdots\)
525.3.l.c	$525$	$3$	525.l	5.c	$4$	$16$	$8$	$14.305$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta _{5}+\beta _{9})q^{2}+\beta _{13}q^{3}+(2\beta _{3}+\beta _{12}+\cdots)q^{4}+\cdots\)
525.3.l.d	$525$	$3$	525.l	5.c	$4$	$16$	$8$	$14.305$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{14}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta _{1}-\beta _{6})q^{2}-\beta _{2}q^{3}+(-\beta _{4}-3\beta _{7}+\cdots)q^{4}+\cdots\)
525.3.l.e	$525$	$3$	525.l	5.c	$4$	$24$	$12$	$14.305$		None		$2$	$0$	\(-8\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{3}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)