Space of modular forms of level 45, weight 7, and Character 45.d

• Label: 45.7.d
• Level: $45$
• Weight: $7$
• Character orbit: 45.d
• Rep. character: $\chi_{45}(44,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $42$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	45.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(42\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(45, [\chi])\).

	Total	New	Old
Modular forms	40	12	28
Cusp forms	32	12	20
Eisenstein series	8	0	8

Trace form

\( 12 q + 516 q^{4} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(45, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
45.7.d.a	$45$	$7$	45.d	15.d	$2$	$12$	$12$	$10.352$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	45.7.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{20}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{2}+(43-\beta _{1})q^{4}+(\beta _{6}+\beta _{7})q^{5}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(45, [\chi]) \simeq \) \(S_{7}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)