Space of modular forms of level 45, weight 3, and Character 45.g

• Label: 45.3.g
• Level: $45$
• Weight: $3$
• Character orbit: 45.g
• Rep. character: $\chi_{45}(28,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $18$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	45.g (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(18\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(45, [\chi])\).

	Total	New	Old
Modular forms	32	12	20
Cusp forms	16	8	8
Eisenstein series	16	4	12

Trace form

\( 8 q + 4 q^{2} + 4 q^{5} - 16 q^{7} - 12 q^{8} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(45, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
45.3.g.a	$45$	$3$	45.g	5.c	$4$	$4$	$2$	$1.226$	\(\Q(i, \sqrt{10})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-20\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(2\beta _{1}+\beta _{3})q^{5}+(-5+\cdots)q^{7}+\cdots\)
45.3.g.b	$45$	$3$	45.g	5.c	$4$	$4$	$2$	$1.226$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(4\)	\(0\)	\(4\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{1}+\beta _{2})q^{2}+(2\beta _{1}+\beta _{2}+2\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(45, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)