Space of modular forms of level 975, weight 2, and Character 975.bl

• Label: 975.2.bl
• Level: $975$
• Weight: $2$
• Character orbit: 975.bl
• Rep. character: $\chi_{975}(193,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $168$
• Newform subspaces: $9$
• Sturm bound: $280$
• Trace bound: $16$

Defining parameters

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bl (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(280\)
Trace bound:			\(16\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(975, [\chi])\).

	Total	New	Old
Modular forms	608	168	440
Cusp forms	512	168	344
Eisenstein series	96	0	96

Trace form

\( 168 q - 4 q^{2} - 84 q^{4} + 24 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(975, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
975.2.bl.a	$975$	$2$	975.bl	65.o	$12$	$8$	$2$	$7.785$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(2\zeta_{24}-\zeta_{24}^{3}-\zeta_{24}^{5}-\zeta_{24}^{7})q^{2}+\cdots\)
975.2.bl.b	$975$	$2$	975.bl	65.o	$12$	$8$	$2$	$7.785$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\zeta_{24}+\zeta_{24}^{5}+\zeta_{24}^{7})q^{2}+\zeta_{24}^{5}q^{3}+\cdots\)
975.2.bl.c	$975$	$2$	975.bl	65.o	$12$	$8$	$2$	$7.785$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\zeta_{24}+\zeta_{24}^{5}+\zeta_{24}^{7})q^{2}+(-\zeta_{24}^{3}+\cdots)q^{3}+\cdots\)
975.2.bl.d	$975$	$2$	975.bl	65.o	$12$	$8$	$2$	$7.785$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\zeta_{24}^{3}+\zeta_{24}^{5}+\zeta_{24}^{7})q^{2}-\zeta_{24}^{5}q^{3}+\cdots\)
975.2.bl.e	$975$	$2$	975.bl	65.o	$12$	$16$	$4$	$7.785$	16.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\beta _{6}-\beta _{10}-\beta _{13}-\beta _{15})q^{2}+\beta _{10}q^{3}+\cdots\)
975.2.bl.f	$975$	$2$	975.bl	65.o	$12$	$16$	$4$	$7.785$	16.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\beta _{1}+\beta _{6}+\beta _{7}-\beta _{13})q^{2}+(-\beta _{3}+\cdots)q^{3}+\cdots\)
975.2.bl.g	$975$	$2$	975.bl	65.o	$12$	$16$	$4$	$7.785$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\beta _{6}-\beta _{10}-\beta _{11}+\beta _{14})q^{2}+\beta _{6}q^{3}+\cdots\)
975.2.bl.h	$975$	$2$	975.bl	65.o	$12$	$32$	$8$	$7.785$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
975.2.bl.i	$975$	$2$	975.bl	65.o	$12$	$56$	$14$	$7.785$		None		$2$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(975, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(975, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(325, [\chi])\)\(^{\oplus 2}\)