Space of modular forms of level 45, weight 11, and Character 45.d

• Label: 45.11.d
• Level: $45$
• Weight: $11$
• Character orbit: 45.d
• Rep. character: $\chi_{45}(44,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $1$
• Sturm bound: $66$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 11 \)
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:			\(66\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(45, [\chi])\).

	Total	New	Old
Modular forms	64	20	44
Cusp forms	56	20	36
Eisenstein series	8	0	8

Trace form

20 * q + 11460 * q^4 - 338408 * q^10 + 6108820 * q^16 - 1898000 * q^19 + 2383676 * q^25 - 19349480 * q^31 - 195513640 * q^34 - 982288972 * q^40 + 1436848520 * q^46 - 2337029140 * q^49 - 1365616152 * q^55 + 4509875560 * q^61 + 4500285020 * q^64 - 5716509336 * q^70 + 8659186800 * q^76 + 2245667080 * q^79 + 8361269368 * q^85 - 59725577880 * q^91 + 65993506880 * q^94

Decomposition of \(S_{11}^{\mathrm{new}}(45, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
45.11.d.a	$45$	$11$	45.d	15.d	$2$	$20$	$20$	$28.591$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓	✓	✓	45.11.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{21}\cdot 3^{68}\cdot 5^{12}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{10}q^{2}+(573-\beta _{1})q^{4}+(-11\beta _{10}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(45, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)