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

• Label: 525.3.f
• Level: $525$
• Weight: $3$
• Character orbit: 525.f
• Rep. character: $\chi_{525}(449,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $3$
• Sturm bound: $240$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
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	172	72	100
Cusp forms	148	72	76
Eisenstein series	24	0	24

Trace form

\( 72 q + 136 q^{4} + 24 q^{9} + O(q^{10}) \)

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.f.a	$525$	$3$	525.f	15.d	$2$	$8$	$8$	$14.305$	8.0.4337012736.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(-\beta _{2}+\beta _{3}+\beta _{4})q^{3}+(3+\cdots)q^{4}+\cdots\)
525.3.f.b	$525$	$3$	525.f	15.d	$2$	$32$	$32$	$14.305$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
525.3.f.c	$525$	$3$	525.f	15.d	$2$	$32$	$32$	$14.305$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

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