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

• Label: 975.2.h
• Level: $975$
• Weight: $2$
• Character orbit: 975.h
• Rep. character: $\chi_{975}(649,\cdot)$
• Character field: $\Q$
• Dimension: $40$
• Newform subspaces: $9$
• Sturm bound: $280$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(280\)
Trace bound:			\(7\)
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	152	40	112
Cusp forms	128	40	88
Eisenstein series	24	0	24

Trace form

\( 40 q + 36 q^{4} - 40 q^{9} + O(q^{10}) \)

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.h.a	$975$	$2$	975.h	65.d	$2$	$2$	$2$	$7.785$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-iq^{3}-q^{4}+iq^{6}+2q^{7}+3q^{8}+\cdots\)
975.2.h.b	$975$	$2$	975.h	65.d	$2$	$2$	$2$	$7.785$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}-2q^{4}-3q^{7}-q^{9}+3iq^{11}+\cdots\)
975.2.h.c	$975$	$2$	975.h	65.d	$2$	$2$	$2$	$7.785$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-2q^{4}+3q^{7}-q^{9}+3iq^{11}+\cdots\)
975.2.h.d	$975$	$2$	975.h	65.d	$2$	$2$	$2$	$7.785$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+iq^{3}-q^{4}+iq^{6}-2q^{7}-3q^{8}+\cdots\)
975.2.h.e	$975$	$2$	975.h	65.d	$2$	$4$	$4$	$7.785$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(-2\)	\(0\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{3})q^{2}-\beta _{2}q^{3}+(3-\beta _{3})q^{4}+\cdots\)
975.2.h.f	$975$	$2$	975.h	65.d	$2$	$4$	$4$	$7.785$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{12}^{3}q^{2}+\zeta_{12}q^{3}+q^{4}-\zeta_{12}^{2}q^{6}+\cdots\)
975.2.h.g	$975$	$2$	975.h	65.d	$2$	$4$	$4$	$7.785$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(2\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{3})q^{2}-\beta _{2}q^{3}+(3-\beta _{3})q^{4}+\cdots\)
975.2.h.h	$975$	$2$	975.h	65.d	$2$	$8$	$8$	$7.785$	8.0.3057647616.6	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+\beta _{6}q^{6}+\cdots\)
975.2.h.i	$975$	$2$	975.h	65.d	$2$	$12$	$12$	$7.785$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{7}q^{3}+(1-\beta _{2})q^{4}-\beta _{6}q^{6}+\cdots\)

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

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