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

• Label: 945.2.k
• Level: $945$
• Weight: $2$
• Character orbit: 945.k
• Rep. character: $\chi_{945}(361,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $64$
• Newform subspaces: $3$
• Sturm bound: $288$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.k (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(288\)
Trace bound:			\(1\)
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	64	248
Cusp forms	264	64	200
Eisenstein series	48	0	48

Trace form

64 * q - 32 * q^4 - 8 * q^5 - 2 * q^7 + 4 * q^11 + 2 * q^13 + 18 * q^14 - 32 * q^16 + 16 * q^17 - 4 * q^19 + 12 * q^20 - 12 * q^23 + 64 * q^25 + 8 * q^26 - 8 * q^28 + 10 * q^29 + 8 * q^31 - 20 * q^32 + 2 * q^37 - 88 * q^38 - 10 * q^41 + 8 * q^43 + 14 * q^44 - 6 * q^46 + 52 * q^47 - 14 * q^49 - 16 * q^52 - 102 * q^56 + 10 * q^59 + 8 * q^61 + 24 * q^62 + 64 * q^64 - 2 * q^65 + 14 * q^67 - 116 * q^68 + 6 * q^70 - 48 * q^71 - 28 * q^73 + 88 * q^74 - 16 * q^76 - 10 * q^77 + 8 * q^79 + 28 * q^80 + 68 * q^83 + 6 * q^85 + 4 * q^86 + 14 * q^89 - 22 * q^91 + 100 * q^92 + 12 * q^94 + 2 * q^97 + 10 * q^98

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.k.a	$945$	$2$	945.k	63.g	$3$	$4$	$2$	$7.546$	\(\Q(\sqrt{-3}, \sqrt{13})\)	None					315.2.k.a	$2$	$0$	\(-1\)	\(0\)	\(4\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
945.2.k.b	$945$	$2$	945.k	63.g	$3$	$24$	$12$	$7.546$		None					315.2.k.b	$2$	$0$	\(1\)	\(0\)	\(24\)	\(7\)		$\mathrm{SU}(2)[C_{3}]$
945.2.k.c	$945$	$2$	945.k	63.g	$3$	$36$	$18$	$7.546$		None			✓		315.2.k.c	$2$	$0$	\(0\)	\(0\)	\(-36\)	\(-1\)		$\mathrm{SU}(2)[C_{3}]$

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

\( S_{2}^{\mathrm{old}}(945, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(189, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)