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

• Label: 975.2.s
• Level: $975$
• Weight: $2$
• Character orbit: 975.s
• Rep. character: $\chi_{975}(818,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $160$
• Newform subspaces: $6$
• Sturm bound: $280$
• Trace bound: $36$

Defining parameters

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.s (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 195 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(280\)
Trace bound:			\(36\)
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	176	128
Cusp forms	256	160	96
Eisenstein series	48	16	32

Trace form

\( 160 q + 4 q^{3} + O(q^{10}) \)

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.s.a	$975$	$2$	975.s	195.s	$4$	$8$	$4$	$7.785$	\(\Q(\zeta_{24})\)	\(\Q(\sqrt{-3}) \)		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5^{4}$	$\mathrm{U}(1)[D_{4}]$	\(q+\zeta_{24}^{4}q^{3}-2\zeta_{24}^{2}q^{4}+(\zeta_{24}+2\zeta_{24}^{6}+\cdots)q^{7}+\cdots\)
975.2.s.b	$975$	$2$	975.s	195.s	$4$	$8$	$4$	$7.785$	8.0.\(\cdots\).2	\(\Q(\sqrt{-195}) \)		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{U}(1)[D_{4}]$	\(q-\beta _{3}q^{3}+2\beta _{2}q^{4}+\beta _{1}q^{7}-3\beta _{2}q^{9}+\cdots\)
975.2.s.c	$975$	$2$	975.s	195.s	$4$	$16$	$8$	$7.785$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	\(\Q(\sqrt{-39}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 5^{2}$	$\mathrm{U}(1)[D_{4}]$	\(q+\beta _{1}q^{2}+\beta _{3}q^{3}+(2\beta _{2}+\beta _{10})q^{4}+\cdots\)
975.2.s.d	$975$	$2$	975.s	195.s	$4$	$32$	$16$	$7.785$		None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
975.2.s.e	$975$	$2$	975.s	195.s	$4$	$32$	$16$	$7.785$		None		$8$	$0$	\(0\)	\(4\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$
975.2.s.f	$975$	$2$	975.s	195.s	$4$	$64$	$32$	$7.785$		None		$16$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

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