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

• Label: 945.2.j
• Level: $945$
• Weight: $2$
• Character orbit: 945.j
• Rep. character: $\chi_{945}(541,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $84$
• Newform subspaces: $10$
• Sturm bound: $288$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.j (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 7 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(288\)
Trace bound:			\(7\)
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	84	228
Cusp forms	264	84	180
Eisenstein series	48	0	48

Trace form

\( 84 q - 40 q^{4} - 14 q^{7} + O(q^{10}) \)

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.j.a	$945$	$2$	945.j	7.c	$3$	$2$	$1$	$7.546$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}-\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
945.2.j.b	$945$	$2$	945.j	7.c	$3$	$2$	$1$	$7.546$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(1\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+\zeta_{6}q^{5}+(1-3\zeta_{6})q^{7}+\cdots\)
945.2.j.c	$945$	$2$	945.j	7.c	$3$	$6$	$3$	$7.546$	6.0.1783323.2	None		$2$	$0$	\(-1\)	\(0\)	\(3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-\beta _{3}-\beta _{4}+\beta _{5})q^{4}+(1+\cdots)q^{5}+\cdots\)
945.2.j.d	$945$	$2$	945.j	7.c	$3$	$6$	$3$	$7.546$	6.0.1783323.2	None		$2$	$0$	\(1\)	\(0\)	\(-3\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-\beta _{3}-\beta _{4}+\beta _{5})q^{4}+(-1+\cdots)q^{5}+\cdots\)
945.2.j.e	$945$	$2$	945.j	7.c	$3$	$10$	$5$	$7.546$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(-5\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(\beta _{2}-\beta _{6}+\beta _{9})q^{4}+(-1+\cdots)q^{5}+\cdots\)
945.2.j.f	$945$	$2$	945.j	7.c	$3$	$10$	$5$	$7.546$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-5\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{2})q^{2}+(-1+\beta _{3}+\beta _{6}-\beta _{8}+\cdots)q^{4}+\cdots\)
945.2.j.g	$945$	$2$	945.j	7.c	$3$	$10$	$5$	$7.546$	10.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(5\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{6}-\beta _{9})q^{4}+\cdots\)
945.2.j.h	$945$	$2$	945.j	7.c	$3$	$10$	$5$	$7.546$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(5\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}+\beta _{2})q^{2}+(-1+\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
945.2.j.i	$945$	$2$	945.j	7.c	$3$	$14$	$7$	$7.546$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-7\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{2})q^{2}+(\beta _{3}-\beta _{7}+\beta _{10}+\cdots)q^{4}+\cdots\)
945.2.j.j	$945$	$2$	945.j	7.c	$3$	$14$	$7$	$7.546$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(7\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{2})q^{2}+(\beta _{3}-\beta _{7}+\beta _{10})q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(945, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)