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

• Label: 945.2.bq
• Level: $945$
• Weight: $2$
• Character orbit: 945.bq
• Rep. character: $\chi_{945}(719,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $88$
• 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.bq (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 315 \)
Character field:			\(\Q(\zeta_{6})\)
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	312	104	208
Cusp forms	264	88	176
Eisenstein series	48	16	32

Trace form

88 * q + 76 * q^4 + 3 * q^5 - 6 * q^10 + 12 * q^11 + 12 * q^14 + 52 * q^16 - 12 * q^19 + 6 * q^20 + q^25 + 12 * q^26 - 6 * q^29 - 12 * q^34 - 30 * q^40 - 6 * q^41 + 84 * q^44 - 18 * q^46 - 8 * q^49 - 30 * q^50 + 78 * q^56 + 12 * q^59 - 8 * q^64 + 15 * q^70 + 30 * q^74 - 48 * q^76 - 16 * q^79 + 69 * q^80 - 7 * q^85 + 12 * q^86 - 72 * q^89 + 20 * q^91

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
945.2.bq.a	$945$	$2$	945.bq	315.aq	$6$	$88$	$44$	$7.546$		None			✓	✓	315.2.u.a	$4$	$0$	\(0\)	\(0\)	\(3\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

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