Space of modular forms of level 45, weight 4, and Character 45.f

• Label: 45.4.f
• Level: $45$
• Weight: $4$
• Character orbit: 45.f
• Rep. character: $\chi_{45}(8,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	45.f (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(45, [\chi])\).

	Total	New	Old
Modular forms	44	12	32
Cusp forms	28	12	16
Eisenstein series	16	0	16

Trace form

12 * q + 24 * q^7 + 192 * q^10 - 108 * q^13 - 648 * q^16 + 1056 * q^22 - 144 * q^25 - 576 * q^28 - 1248 * q^31 + 828 * q^37 + 2568 * q^40 - 96 * q^43 + 672 * q^46 - 312 * q^52 - 1512 * q^55 - 3864 * q^58 + 96 * q^61 + 1632 * q^67 - 1536 * q^70 + 3972 * q^73 - 480 * q^76 - 7848 * q^82 - 1752 * q^85 + 7968 * q^88 + 4752 * q^91 + 2772 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(45, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
45.4.f.a	$45$	$4$	45.f	15.e	$4$	$12$	$6$	$2.655$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓	✓	45.4.f.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(24\)	$2^{10}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q+\beta _{6}q^{2}+(-6\beta _{1}+\beta _{5})q^{4}+(\beta _{9}+\beta _{10}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(45, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)