Space of modular forms of level 45, weight 5, and Character 45.d

• Label: 45.5.d
• Level: $45$
• Weight: $5$
• Character orbit: 45.d
• Rep. character: $\chi_{45}(44,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $30$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
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:			\(30\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(45, [\chi])\).

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

Trace form

8 * q + 36 * q^4 + 280 * q^10 + 148 * q^16 - 1520 * q^19 + 1940 * q^25 + 2968 * q^31 - 12424 * q^34 + 7220 * q^40 + 10088 * q^46 - 8944 * q^49 + 19800 * q^55 + 544 * q^61 - 29188 * q^64 + 1800 * q^70 + 3600 * q^76 - 12632 * q^79 - 3260 * q^85 - 24552 * q^91 + 40928 * q^94

Decomposition of \(S_{5}^{\mathrm{new}}(45, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
45.5.d.a	$45$	$5$	45.d	15.d	$2$	$8$	$8$	$4.652$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		✓	✓	✓	45.5.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{2}+(5+\beta _{2})q^{4}+(2\beta _{3}+\beta _{5})q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(45, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)