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

• Label: 525.2.r
• Level: $525$
• Weight: $2$
• Character orbit: 525.r
• Rep. character: $\chi_{525}(424,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $48$
• Newform subspaces: $8$
• Sturm bound: $160$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.r (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(160\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(2\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	184	48	136
Cusp forms	136	48	88
Eisenstein series	48	0	48

Trace form

\( 48 q + 24 q^{4} + 8 q^{6} + 24 q^{9} + O(q^{10}) \)

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.r.a	$525$	$2$	525.r	35.j	$6$	$4$	$2$	$4.192$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(-6\)	\(0\)	\(0\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+\cdots\)
525.2.r.b	$525$	$2$	525.r	35.j	$6$	$4$	$2$	$4.192$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{3}+(-2+2\zeta_{12}^{2})q^{4}+(-\zeta_{12}+\cdots)q^{7}+\cdots\)
525.2.r.c	$525$	$2$	525.r	35.j	$6$	$4$	$2$	$4.192$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}-\zeta_{12}^{2}q^{4}+\cdots\)
525.2.r.d	$525$	$2$	525.r	35.j	$6$	$4$	$2$	$4.192$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+2\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+2\zeta_{12}^{2}q^{4}+\cdots\)
525.2.r.e	$525$	$2$	525.r	35.j	$6$	$4$	$2$	$4.192$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+2\zeta_{12}q^{2}+(\zeta_{12}-\zeta_{12}^{3})q^{3}+2\zeta_{12}^{2}q^{4}+\cdots\)
525.2.r.f	$525$	$2$	525.r	35.j	$6$	$4$	$2$	$4.192$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(6\)	\(0\)	\(0\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-\zeta_{12}q^{3}+\cdots\)
525.2.r.g	$525$	$2$	525.r	35.j	$6$	$8$	$4$	$4.192$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\zeta_{24}^{5}q^{2}-\zeta_{24}q^{3}+\zeta_{24}^{7}q^{6}+(\zeta_{24}+\cdots)q^{7}+\cdots\)
525.2.r.h	$525$	$2$	525.r	35.j	$6$	$16$	$8$	$4.192$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+\beta _{12}q^{3}+(1+\beta _{3}+2\beta _{5}+\cdots)q^{4}+\cdots\)

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

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