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

• Label: 945.2.i
• Level: $945$
• Weight: $2$
• Character orbit: 945.i
• Rep. character: $\chi_{945}(316,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $48$
• Newform subspaces: $6$
• Sturm bound: $288$
• Trace bound: $5$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	312	48	264
Cusp forms	264	48	216
Eisenstein series	48	0	48

Trace form

\( 48 q - 4 q^{2} - 24 q^{4} + O(q^{10}) \)

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.i.a	$945$	$2$	945.i	9.c	$3$	$2$	$1$	$7.546$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
945.2.i.b	$945$	$2$	945.i	9.c	$3$	$2$	$1$	$7.546$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(-1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
945.2.i.c	$945$	$2$	945.i	9.c	$3$	$8$	$4$	$7.546$	\(\Q(\zeta_{15})\)	None		$2$	$0$	\(-1\)	\(0\)	\(-4\)	\(4\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1-\zeta_{15}+\zeta_{15}^{2}-\zeta_{15}^{3})q^{2}+\cdots\)
945.2.i.d	$945$	$2$	945.i	9.c	$3$	$8$	$4$	$7.546$	8.0.142635249.1	None		$2$	$0$	\(-1\)	\(0\)	\(4\)	\(-4\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{7}q^{2}+(\beta _{1}+\beta _{4}+\beta _{7})q^{4}+(1-\beta _{2}+\cdots)q^{5}+\cdots\)
945.2.i.e	$945$	$2$	945.i	9.c	$3$	$12$	$6$	$7.546$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		$2$	$0$	\(-3\)	\(0\)	\(-6\)	\(-6\)	$3^{3}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\beta _{1}+\beta _{4}-\beta _{5})q^{2}+(-2-\beta _{2}+\cdots)q^{4}+\cdots\)
945.2.i.f	$945$	$2$	945.i	9.c	$3$	$16$	$8$	$7.546$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-1\)	\(0\)	\(8\)	\(8\)	$3^{8}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{13})q^{2}+(-\beta _{3}-\beta _{10})q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(945, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)