Space of modular forms of level 525, weight 2, and Character 525.j

• Label: 525.2.j
• Level: $525$
• Weight: $2$
• Character orbit: 525.j
• Rep. character: $\chi_{525}(218,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $72$
• Newform subspaces: $3$
• Sturm bound: $160$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(160\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(525, [\chi])\).

	Total	New	Old
Modular forms	184	72	112
Cusp forms	136	72	64
Eisenstein series	48	0	48

Trace form

\( 72 q + 4 q^{3} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(525, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
525.2.j.a	$525$	$2$	525.j	15.e	$4$	$16$	$8$	$4.192$	16.0.\(\cdots\).1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta _{10}+\beta _{13}-\beta _{15})q^{2}+\beta _{7}q^{3}+\cdots\)
525.2.j.b	$525$	$2$	525.j	15.e	$4$	$24$	$12$	$4.192$		None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
525.2.j.c	$525$	$2$	525.j	15.e	$4$	$32$	$16$	$4.192$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(525, [\chi])\) into lower level spaces

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