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

• Label: 975.2.bb
• Level: $975$
• Weight: $2$
• Character orbit: 975.bb
• Rep. character: $\chi_{975}(724,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $88$
• Newform subspaces: $12$
• Sturm bound: $280$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bb (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(280\)
Trace bound:			\(14\)
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	304	88	216
Cusp forms	256	88	168
Eisenstein series	48	0	48

Trace form

\( 88 q + 48 q^{4} + 44 q^{9} + O(q^{10}) \)

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.bb.a	$975$	$2$	975.bb	65.n	$6$	$4$	$2$	$7.785$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(-6\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+\zeta_{12}-\zeta_{12}^{2})q^{2}+\zeta_{12}q^{3}+\cdots\)
975.2.bb.b	$975$	$2$	975.bb	65.n	$6$	$4$	$2$	$7.785$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}+\zeta_{12}^{3})q^{3}+(-2+2\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
975.2.bb.c	$975$	$2$	975.bb	65.n	$6$	$4$	$2$	$7.785$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+\zeta_{12}^{2}q^{6}+\cdots\)
975.2.bb.d	$975$	$2$	975.bb	65.n	$6$	$4$	$2$	$7.785$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+\zeta_{12}^{2}q^{6}+\cdots\)
975.2.bb.e	$975$	$2$	975.bb	65.n	$6$	$4$	$2$	$7.785$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{2}+\zeta_{12}q^{3}-\zeta_{12}^{2}q^{4}+\zeta_{12}^{2}q^{6}+\cdots\)
975.2.bb.f	$975$	$2$	975.bb	65.n	$6$	$4$	$2$	$7.785$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+2\zeta_{12}q^{2}-\zeta_{12}q^{3}+2\zeta_{12}^{2}q^{4}+\cdots\)
975.2.bb.g	$975$	$2$	975.bb	65.n	$6$	$4$	$2$	$7.785$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+2\zeta_{12}q^{2}-\zeta_{12}q^{3}+2\zeta_{12}^{2}q^{4}+\cdots\)
975.2.bb.h	$975$	$2$	975.bb	65.n	$6$	$4$	$2$	$7.785$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(6\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
975.2.bb.i	$975$	$2$	975.bb	65.n	$6$	$8$	$4$	$7.785$	8.0.1731891456.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(2+3\beta _{2}-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
975.2.bb.j	$975$	$2$	975.bb	65.n	$6$	$12$	$6$	$7.785$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{5}+\beta _{9})q^{2}+(\beta _{3}+\beta _{4})q^{3}+(1-\beta _{8}+\cdots)q^{4}+\cdots\)
975.2.bb.k	$975$	$2$	975.bb	65.n	$6$	$12$	$6$	$7.785$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{8}q^{2}-\beta _{6}q^{3}+(1+3\beta _{2}-2\beta _{3}+\cdots)q^{4}+\cdots\)
975.2.bb.l	$975$	$2$	975.bb	65.n	$6$	$24$	$12$	$7.785$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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