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

• Label: 975.2.bh
• Level: $975$
• Weight: $2$
• Character orbit: 975.bh
• Rep. character: $\chi_{975}(181,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $272$
• Newform subspaces: $3$
• Sturm bound: $280$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bh (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 325 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(280\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	576	272	304
Cusp forms	544	272	272
Eisenstein series	32	0	32

Trace form

\( 272 q + 64 q^{4} - 68 q^{9} + O(q^{10}) \)

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.bh.a	$975$	$2$	975.bh	325.q	$10$	$8$	$2$	$7.785$	\(\Q(\zeta_{20})\)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{10}]$	\(q+(\zeta_{20}+\zeta_{20}^{3}-\zeta_{20}^{5}-\zeta_{20}^{7})q^{2}+\cdots\)
975.2.bh.b	$975$	$2$	975.bh	325.q	$10$	$128$	$32$	$7.785$		None		$4$	$0$	\(0\)	\(-32\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$
975.2.bh.c	$975$	$2$	975.bh	325.q	$10$	$136$	$34$	$7.785$		None		$4$	$0$	\(0\)	\(34\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

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

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