Space of modular forms of level 45, weight 2, and Character 45.l

• Label: 45.2.l
• Level: $45$
• Weight: $2$
• Character orbit: 45.l
• Rep. character: $\chi_{45}(2,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	45.l (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 45 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(45, [\chi])\).

	Total	New	Old
Modular forms	32	32	0
Cusp forms	16	16	0
Eisenstein series	16	16	0

Trace form

\( 16 q - 6 q^{2} - 6 q^{3} - 6 q^{5} - 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(45, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
45.2.l.a	$45$	$2$	45.l	45.l	$12$	$16$	$4$	$0.359$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$4$	$0$	\(-6\)	\(-6\)	\(-6\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q-\beta _{5}q^{2}+(-1+\beta _{9}-\beta _{11}-\beta _{12}+\cdots)q^{3}+\cdots\)