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

• Label: 525.2.bf
• Level: $525$
• Weight: $2$
• Character orbit: 525.bf
• Rep. character: $\chi_{525}(32,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $176$
• Newform subspaces: $7$
• Sturm bound: $160$
• Trace bound: $21$

Defining parameters

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bf (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(160\)
Trace bound:			\(21\)
Distinguishing \(T_p\):			\(2\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	368	208	160
Cusp forms	272	176	96
Eisenstein series	96	32	64

Trace form

\( 176 q + 2 q^{3} + 12 q^{7} + O(q^{10}) \)

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.bf.a	$525$	$2$	525.bf	105.x	$12$	$8$	$2$	$4.192$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(-4\)	\(4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-1+\zeta_{24}^{2}+\zeta_{24}^{4})q^{2}+(-\zeta_{24}+\cdots)q^{3}+\cdots\)
525.2.bf.b	$525$	$2$	525.bf	105.x	$12$	$8$	$2$	$4.192$	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-3}) \)		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(2\zeta_{24}-\zeta_{24}^{5})q^{3}+2\zeta_{24}^{2}q^{4}+(-2\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
525.2.bf.c	$525$	$2$	525.bf	105.x	$12$	$8$	$2$	$4.192$	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-3}) \)		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(2\zeta_{24}-\zeta_{24}^{5})q^{3}+2\zeta_{24}^{2}q^{4}+(3\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
525.2.bf.d	$525$	$2$	525.bf	105.x	$12$	$8$	$2$	$4.192$	\(\Q(\zeta_{24})\)	None		$8$	$0$	\(4\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(1-\zeta_{24}^{2}-\zeta_{24}^{4})q^{2}+(\zeta_{24}+\zeta_{24}^{2}+\cdots)q^{3}+\cdots\)
525.2.bf.e	$525$	$2$	525.bf	105.x	$12$	$16$	$4$	$4.192$	16.0.\(\cdots\).4	None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\beta _{5}+\beta _{6}+\beta _{9})q^{2}+\beta _{15}q^{3}-3\beta _{7}q^{4}+\cdots\)
525.2.bf.f	$525$	$2$	525.bf	105.x	$12$	$48$	$12$	$4.192$		None		$8$	$0$	\(0\)	\(2\)	\(0\)	\(12\)		$\mathrm{SU}(2)[C_{12}]$
525.2.bf.g	$525$	$2$	525.bf	105.x	$12$	$80$	$20$	$4.192$		None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

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