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

• Label: 975.2.bo
• Level: $975$
• Weight: $2$
• Character orbit: 975.bo
• Rep. character: $\chi_{975}(176,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $332$
• Newform subspaces: $8$
• Sturm bound: $280$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bo (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(280\)
Trace bound:			\(19\)
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	380	228
Cusp forms	512	332	180
Eisenstein series	96	48	48

Trace form

\( 332 q + 2 q^{3} + 12 q^{4} - 2 q^{6} + 2 q^{7} + 2 q^{9} + O(q^{10}) \)

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.bo.a	$975$	$2$	975.bo	39.k	$12$	$4$	$1$	$7.785$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-10\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+2\zeta_{12}q^{4}+(-3+\cdots)q^{7}+\cdots\)
975.2.bo.b	$975$	$2$	975.bo	39.k	$12$	$4$	$1$	$7.785$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(10\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+2\zeta_{12}q^{4}+(3+\cdots)q^{7}+\cdots\)
975.2.bo.c	$975$	$2$	975.bo	39.k	$12$	$4$	$1$	$7.785$	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(10\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(\zeta_{12}+\zeta_{12}^{3})q^{3}+2\zeta_{12}q^{4}+(2+2\zeta_{12}+\cdots)q^{7}+\cdots\)
975.2.bo.d	$975$	$2$	975.bo	39.k	$12$	$8$	$2$	$7.785$	8.0.56070144.2	None		$4$	$0$	\(0\)	\(2\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+2\beta _{5}+\beta _{7})q^{2}+\cdots\)
975.2.bo.e	$975$	$2$	975.bo	39.k	$12$	$72$	$18$	$7.785$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)		$\mathrm{SU}(2)[C_{12}]$
975.2.bo.f	$975$	$2$	975.bo	39.k	$12$	$72$	$18$	$7.785$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
975.2.bo.g	$975$	$2$	975.bo	39.k	$12$	$72$	$18$	$7.785$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$
975.2.bo.h	$975$	$2$	975.bo	39.k	$12$	$96$	$24$	$7.785$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

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

\( S_{2}^{\mathrm{old}}(975, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)