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

• Label: 945.2.bj
• Level: $945$
• Weight: $2$
• Character orbit: 945.bj
• Rep. character: $\chi_{945}(26,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $84$
• Newform subspaces: $12$
• Sturm bound: $288$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.bj (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(288\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(11\)

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.bj.a	$945$	$2$	945.bj	21.g	$6$	$2$	$1$	$7.546$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-3\)	\(0\)	\(-1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\zeta_{6})q^{2}+(1-\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots\)
945.2.bj.b	$945$	$2$	945.bj	21.g	$6$	$2$	$1$	$7.546$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-3\)	\(0\)	\(1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\zeta_{6})q^{2}+(1-\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots\)
945.2.bj.c	$945$	$2$	945.bj	21.g	$6$	$2$	$1$	$7.546$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(3\)	\(0\)	\(-1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\zeta_{6})q^{2}+(1-\zeta_{6})q^{4}-\zeta_{6}q^{5}+\cdots\)
945.2.bj.d	$945$	$2$	945.bj	21.g	$6$	$2$	$1$	$7.546$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(3\)	\(0\)	\(1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\zeta_{6})q^{2}+(1-\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots\)
945.2.bj.e	$945$	$2$	945.bj	21.g	$6$	$4$	$2$	$7.546$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(-3\)	\(0\)	\(2\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\beta _{3})q^{2}+(2-\beta _{1}-\beta _{2}+2\beta _{3})q^{4}+\cdots\)
945.2.bj.f	$945$	$2$	945.bj	21.g	$6$	$4$	$2$	$7.546$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		$2$	$0$	\(3\)	\(0\)	\(-2\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
945.2.bj.g	$945$	$2$	945.bj	21.g	$6$	$6$	$3$	$7.546$	6.0.309123.1	None		$2$	$0$	\(-3\)	\(0\)	\(-3\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\beta _{3})q^{2}+(-\beta _{2}+\beta _{5})q^{4}+\beta _{4}q^{5}+\cdots\)
945.2.bj.h	$945$	$2$	945.bj	21.g	$6$	$6$	$3$	$7.546$	6.0.309123.1	None		$2$	$0$	\(3\)	\(0\)	\(3\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\beta _{3})q^{2}+(-\beta _{2}+\beta _{5})q^{4}-\beta _{4}q^{5}+\cdots\)
945.2.bj.i	$945$	$2$	945.bj	21.g	$6$	$8$	$4$	$7.546$	8.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}-\beta _{2})q^{2}+(2-\beta _{1}-2\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
945.2.bj.j	$945$	$2$	945.bj	21.g	$6$	$8$	$4$	$7.546$	8.0.\(\cdots\).1	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(\beta _{1}-\beta _{3}+2\beta _{4}-\beta _{5}-\beta _{6}+\cdots)q^{4}+\cdots\)
945.2.bj.k	$945$	$2$	945.bj	21.g	$6$	$20$	$10$	$7.546$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-10\)	\(6\)	$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{1}+\beta _{8})q^{2}+(1-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
945.2.bj.l	$945$	$2$	945.bj	21.g	$6$	$20$	$10$	$7.546$	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(10\)	\(6\)	$3^{6}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{8}q^{2}+(\beta _{3}+\beta _{4})q^{4}+(1-\beta _{4})q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(945, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)