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

• Label: 525.2.i
• Level: $525$
• Weight: $2$
• Character orbit: 525.i
• Rep. character: $\chi_{525}(151,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $50$
• Newform subspaces: $11$
• Sturm bound: $160$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(160\)
Trace bound:			\(2\)
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	50	134
Cusp forms	136	50	86
Eisenstein series	48	0	48

Trace form

\( 50 q - 2 q^{2} - q^{3} - 26 q^{4} - 4 q^{6} + 3 q^{7} + 24 q^{8} - 25 q^{9} + O(q^{10}) \)

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

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

\( S_{2}^{\mathrm{old}}(525, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 3}\)