Space of modular forms of level 945, weight 2, and Character 945.by

• Label: 945.2.by
• Level: $945$
• Weight: $2$
• Character orbit: 945.by
• Rep. character: $\chi_{945}(233,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $176$
• Newform subspaces: $1$
• Sturm bound: $288$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.by (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 315 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(288\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(945, [\chi])\).

	Total	New	Old
Modular forms	624	208	416
Cusp forms	528	176	352
Eisenstein series	96	32	64

Trace form

\( 176 q + 6 q^{5} - 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(945, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
945.2.by.a	$945$	$2$	945.by	315.av	$12$	$176$	$44$	$7.546$		None		$4$	$0$	\(0\)	\(0\)	\(6\)	\(-2\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(945, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(945, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)