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

• Label: 945.2.bt
• Level: $945$
• Weight: $2$
• Character orbit: 945.bt
• Rep. character: $\chi_{945}(106,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $432$
• Newform subspaces: $4$
• Sturm bound: $288$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bt (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(288\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	888	432	456
Cusp forms	840	432	408
Eisenstein series	48	0	48

Trace form

\( 432 q + 36 q^{8} + 6 q^{9} + O(q^{10}) \)

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.bt.a	$945$	$2$	945.bt	27.e	$9$	$96$	$16$	$7.546$		None		$2$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$
945.2.bt.b	$945$	$2$	945.bt	27.e	$9$	$96$	$16$	$7.546$		None		$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$
945.2.bt.c	$945$	$2$	945.bt	27.e	$9$	$120$	$20$	$7.546$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$
945.2.bt.d	$945$	$2$	945.bt	27.e	$9$	$120$	$20$	$7.546$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$

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

\( S_{2}^{\mathrm{old}}(945, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)