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

• Label: 975.2.m
• Level: $975$
• Weight: $2$
• Character orbit: 975.m
• Rep. character: $\chi_{975}(443,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $144$
• Newform subspaces: $4$
• Sturm bound: $280$
• Trace bound: $9$

Defining parameters

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.m (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(280\)
Trace bound:			\(9\)
Distinguishing \(T_p\):			\(2\), \(29\)

Dimensions

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

	Total	New	Old
Modular forms	304	144	160
Cusp forms	256	144	112
Eisenstein series	48	0	48

Trace form

\( 144 q + 4 q^{3} + 16 q^{6} + 8 q^{7} + O(q^{10}) \)

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.m.a	$975$	$2$	975.m	15.e	$4$	$32$	$16$	$7.785$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
975.2.m.b	$975$	$2$	975.m	15.e	$4$	$32$	$16$	$7.785$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
975.2.m.c	$975$	$2$	975.m	15.e	$4$	$32$	$16$	$7.785$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
975.2.m.d	$975$	$2$	975.m	15.e	$4$	$48$	$24$	$7.785$		None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(8\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(975, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(75, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)