Space of modular forms of level 45, weight 18, and Character 45.b

• Label: 45.18.b
• Level: $45$
• Weight: $18$
• Character orbit: 45.b
• Rep. character: $\chi_{45}(19,\cdot)$
• Character field: $\Q$
• Dimension: $42$
• Newform subspaces: $4$
• Sturm bound: $108$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	45.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(108\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(45, [\chi])\).

	Total	New	Old
Modular forms	106	44	62
Cusp forms	98	42	56
Eisenstein series	8	2	6

Trace form

42 * q - 2697708 * q^4 - 671940 * q^5 - 237167280 * q^10 - 1370682720 * q^11 - 8310420756 * q^14 + 148002952020 * q^16 - 26904615624 * q^19 - 77093884620 * q^20 + 823760122470 * q^25 - 2101322607228 * q^26 + 9427486429224 * q^29 - 1541203370064 * q^31 - 17507697381528 * q^34 - 29476247894640 * q^35 + 54750906782220 * q^40 - 92343908068272 * q^41 - 108240329103084 * q^44 - 214907707175928 * q^46 - 735935290582170 * q^49 + 613372023545400 * q^50 - 996925976737920 * q^55 + 530951814363780 * q^56 - 1790953444861632 * q^59 + 167230526744772 * q^61 - 5103157020938604 * q^64 - 1700623174634280 * q^65 - 1245883093371360 * q^70 - 13502206308241728 * q^71 + 36651551317548084 * q^74 + 28988751704780424 * q^76 + 19524730950574272 * q^79 + 6185983447756260 * q^80 + 9511569008186580 * q^85 - 96546415318668720 * q^86 + 26116245675750672 * q^89 + 178299093978038592 * q^91 + 787477327092000 * q^94 + 230346994071045600 * q^95

Decomposition of \(S_{18}^{\mathrm{new}}(45, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
45.18.b.a	$45$	$18$	45.b	5.b	$2$	$2$	$2$	$82.450$	\(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{-15}) \)		✓			45.18.b.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+67\beta q^{2}+108627q^{4}-5^{8}\beta q^{5}+\cdots\)
45.18.b.b	$45$	$18$	45.b	5.b	$2$	$8$	$8$	$82.450$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None					5.18.b.a	$2$	$0$	\(0\)	\(0\)	\(-379200\)	\(0\)	$2^{21}\cdot 3^{12}\cdot 5^{12}\cdot 11$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-72387+\beta _{3})q^{4}+(-47400+\cdots)q^{5}+\cdots\)
45.18.b.c	$45$	$18$	45.b	5.b	$2$	$16$	$16$	$82.450$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			45.18.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{73}\cdot 3^{42}\cdot 5^{34}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-92073-\beta _{2})q^{4}+(188\beta _{1}+\cdots)q^{5}+\cdots\)
45.18.b.d	$45$	$18$	45.b	5.b	$2$	$16$	$16$	$82.450$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					15.18.b.a	$2$	$0$	\(0\)	\(0\)	\(-292740\)	\(0\)	$2^{35}\cdot 3^{62}\cdot 5^{23}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-53919+\beta _{2})q^{4}+(-18296+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{18}^{\mathrm{old}}(45, [\chi])\) into lower level spaces

\( S_{18}^{\mathrm{old}}(45, [\chi]) \simeq \) \(S_{18}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)