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

• Label: 975.2.c
• Level: $975$
• Weight: $2$
• Character orbit: 975.c
• Rep. character: $\chi_{975}(274,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $11$
• Sturm bound: $280$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 11 \)
Sturm bound:			\(280\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(2\), \(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	152	36	116
Cusp forms	128	36	92
Eisenstein series	24	0	24

Trace form

\( 36 q - 44 q^{4} + 4 q^{6} - 36 q^{9} + O(q^{10}) \)

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.c.a	$975$	$2$	975.c	5.b	$2$	$2$	$2$	$7.785$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}+iq^{3}-2q^{4}-2q^{6}+3iq^{7}+\cdots\)
975.2.c.b	$975$	$2$	975.c	5.b	$2$	$2$	$2$	$7.785$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-iq^{3}-2q^{4}+2q^{6}-3iq^{7}+\cdots\)
975.2.c.c	$975$	$2$	975.c	5.b	$2$	$2$	$2$	$7.785$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-iq^{3}-2q^{4}+2q^{6}-iq^{7}+\cdots\)
975.2.c.d	$975$	$2$	975.c	5.b	$2$	$2$	$2$	$7.785$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}+q^{4}-q^{6}+iq^{7}+3iq^{8}+\cdots\)
975.2.c.e	$975$	$2$	975.c	5.b	$2$	$2$	$2$	$7.785$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}+q^{4}-q^{6}+3iq^{8}+\cdots\)
975.2.c.f	$975$	$2$	975.c	5.b	$2$	$2$	$2$	$7.785$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}+q^{4}-q^{6}-4iq^{7}+\cdots\)
975.2.c.g	$975$	$2$	975.c	5.b	$2$	$2$	$2$	$7.785$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}+q^{4}+q^{6}-3iq^{7}+\cdots\)
975.2.c.h	$975$	$2$	975.c	5.b	$2$	$4$	$4$	$7.785$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\zeta_{8}+\zeta_{8}^{2})q^{2}+\zeta_{8}q^{3}+(-1-2\zeta_{8}^{3})q^{4}+\cdots\)
975.2.c.i	$975$	$2$	975.c	5.b	$2$	$6$	$6$	$7.785$	6.0.399424.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-\beta _{2}q^{3}+(-3+\beta _{4})q^{4}+\beta _{1}q^{6}+\cdots\)
975.2.c.j	$975$	$2$	975.c	5.b	$2$	$6$	$6$	$7.785$	6.0.5089536.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+\beta _{4}q^{3}+(-2+\beta _{3})q^{4}-\beta _{1}q^{6}+\cdots\)
975.2.c.k	$975$	$2$	975.c	5.b	$2$	$6$	$6$	$7.785$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{5})q^{2}-\beta _{3}q^{3}+(-2-\beta _{1}+\cdots)q^{4}+\cdots\)

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

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