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

• Label: 945.2.b
• Level: $945$
• Weight: $2$
• Character orbit: 945.b
• Rep. character: $\chi_{945}(566,\cdot)$
• Character field: $\Q$
• Dimension: $44$
• Newform subspaces: $4$
• Sturm bound: $288$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	945.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(288\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	156	44	112
Cusp forms	132	44	88
Eisenstein series	24	0	24

Trace form

\( 44 q - 48 q^{4} + 2 q^{7} + O(q^{10}) \)

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.b.a	$945$	$2$	945.b	21.c	$2$	$10$	$10$	$7.546$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-10\)	\(3\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-q^{5}-\beta _{8}q^{7}+\cdots\)
945.2.b.b	$945$	$2$	945.b	21.c	$2$	$10$	$10$	$7.546$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(10\)	\(3\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+q^{5}-\beta _{7}q^{7}+\cdots\)
945.2.b.c	$945$	$2$	945.b	21.c	$2$	$12$	$12$	$7.546$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-12\)	\(-2\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-q^{5}+\beta _{6}q^{7}+\cdots\)
945.2.b.d	$945$	$2$	945.b	21.c	$2$	$12$	$12$	$7.546$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(12\)	\(-2\)	$2\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1+\beta _{2})q^{4}+q^{5}-\beta _{7}q^{7}+\cdots\)

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

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