Space of modular forms of level 45 and weight 6

• Label: 45.6
• Level: 45
• Weight: 6
• Dimension: 249
• Nonzero newspaces: 6
• Newform subspaces: 15
• Sturm bound: 864
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 15 \)
Sturm bound:			\(864\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(45))\).

	Total	New	Old
Modular forms	392	275	117
Cusp forms	328	249	79
Eisenstein series	64	26	38

Trace form

249 * q - 20 * q^2 + 16 * q^3 + 34 * q^4 - 141 * q^5 - 358 * q^6 + 212 * q^7 + 1968 * q^8 + 944 * q^9 - 2414 * q^10 - 3188 * q^11 - 5200 * q^12 + 1466 * q^13 + 5148 * q^14 + 4216 * q^15 + 3530 * q^16 + 6658 * q^17 + 11776 * q^18 - 7212 * q^19 - 12940 * q^20 - 15276 * q^21 - 14562 * q^22 - 25476 * q^23 - 13782 * q^24 - 12369 * q^25 + 47788 * q^26 + 30400 * q^27 + 43256 * q^28 + 8342 * q^29 + 10328 * q^30 + 19344 * q^31 + 6062 * q^32 - 18112 * q^33 - 45442 * q^34 - 27064 * q^35 + 51082 * q^36 - 57166 * q^37 - 4754 * q^38 + 11848 * q^39 + 49460 * q^40 + 38762 * q^41 - 69792 * q^42 + 19184 * q^43 - 166540 * q^44 - 106186 * q^45 + 65144 * q^46 + 14776 * q^47 + 82010 * q^48 - 61963 * q^49 - 51230 * q^50 - 424 * q^51 - 227632 * q^52 - 9902 * q^53 + 114794 * q^54 - 1044 * q^55 + 316716 * q^56 + 262612 * q^57 + 400176 * q^58 + 281644 * q^59 + 162512 * q^60 + 80778 * q^61 - 376644 * q^62 - 294588 * q^63 - 376308 * q^64 - 312224 * q^65 - 165500 * q^66 - 247144 * q^67 - 395506 * q^68 + 20304 * q^69 - 356406 * q^70 + 152384 * q^71 - 200598 * q^72 + 119894 * q^73 + 774908 * q^74 + 373864 * q^75 + 910502 * q^76 + 534840 * q^77 + 561476 * q^78 - 122580 * q^79 + 315032 * q^80 - 193660 * q^81 - 89784 * q^82 - 398880 * q^83 - 782340 * q^84 - 127514 * q^85 - 857450 * q^86 - 208052 * q^87 + 512598 * q^88 + 294138 * q^89 - 746972 * q^90 + 214960 * q^91 - 1054404 * q^92 - 793296 * q^93 - 853756 * q^94 - 709304 * q^95 + 49216 * q^96 - 690094 * q^97 + 853658 * q^98 + 1056748 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(45))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
45.6.a	\(\chi_{45}(1, \cdot)\)	45.6.a.a	1	1
		45.6.a.b	1
		45.6.a.c	1
		45.6.a.d	2
		45.6.a.e	2
		45.6.a.f	2
45.6.b	\(\chi_{45}(19, \cdot)\)	45.6.b.a	2	1
		45.6.b.b	2
		45.6.b.c	4
		45.6.b.d	4
45.6.e	\(\chi_{45}(16, \cdot)\)	45.6.e.a	18	2
		45.6.e.b	22
45.6.f	\(\chi_{45}(8, \cdot)\)	45.6.f.a	20	2
45.6.j	\(\chi_{45}(4, \cdot)\)	45.6.j.a	56	2
45.6.l	\(\chi_{45}(2, \cdot)\)	45.6.l.a	112	4

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(45)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)