Space of modular forms of level 45 and weight 12

• Label: 45.12
• Level: 45
• Weight: 12
• Dimension: 561
• Nonzero newspaces: 6
• Newform subspaces: 17
• Sturm bound: 1728
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 12 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 17 \)
Sturm bound:			\(1728\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(45))\).

	Total	New	Old
Modular forms	824	587	237
Cusp forms	760	561	199
Eisenstein series	64	26	38

Trace form

561 * q + 136 * q^2 + 16 * q^3 + 14482 * q^4 + 8091 * q^5 - 41182 * q^6 - 153564 * q^7 + 376464 * q^8 - 203212 * q^9 - 1107882 * q^10 + 969724 * q^11 + 2089424 * q^12 - 2344738 * q^13 - 10312068 * q^14 + 5015092 * q^15 + 53784714 * q^16 - 58239194 * q^17 - 39107840 * q^18 + 42735964 * q^19 + 74764868 * q^20 - 101769852 * q^21 + 29987942 * q^22 + 62160684 * q^23 + 199409946 * q^24 - 180345633 * q^25 - 420814556 * q^26 + 353644864 * q^27 - 142737816 * q^28 - 18452002 * q^29 - 499220176 * q^30 - 443937400 * q^31 + 1256012174 * q^32 + 742920476 * q^33 + 1639830894 * q^34 - 3298310584 * q^35 - 2638694486 * q^36 - 2998289114 * q^37 + 3477031942 * q^38 + 4986454720 * q^39 + 1309071916 * q^40 - 2552487298 * q^41 - 8017582848 * q^42 - 4914431944 * q^43 + 6729479348 * q^44 + 3492036482 * q^45 - 6503263688 * q^46 - 2850341432 * q^47 + 6690552986 * q^48 + 16662429365 * q^49 - 8589695330 * q^50 - 6273566920 * q^51 - 38908242848 * q^52 - 21331334906 * q^53 - 27551978110 * q^54 + 45395650348 * q^55 + 72050802636 * q^56 + 23914946152 * q^57 - 21080101400 * q^58 - 14816173604 * q^59 - 56768468104 * q^60 - 14060424254 * q^61 - 82825506948 * q^62 - 41929139700 * q^63 + 79535009292 * q^64 + 25744107352 * q^65 + 115757536420 * q^66 - 52569290736 * q^67 + 125486402462 * q^68 - 22350948840 * q^69 + 63173192298 * q^70 - 103189302016 * q^71 - 303190501686 * q^72 - 39547387462 * q^73 + 138945425732 * q^74 - 87888554060 * q^75 + 259857654502 * q^76 + 101172668616 * q^77 - 33211222252 * q^78 - 24203033932 * q^79 + 156834230648 * q^80 - 310892240104 * q^81 - 85864347536 * q^82 - 236909382408 * q^83 + 529108182156 * q^84 + 202516139658 * q^85 + 201798724414 * q^86 - 110782557548 * q^87 - 139755327978 * q^88 - 96664148982 * q^89 + 388701610372 * q^90 - 631279295664 * q^91 + 347617346604 * q^92 + 626122916136 * q^93 + 299293615620 * q^94 - 265823463992 * q^95 - 995328067280 * q^96 - 224650551446 * q^97 - 1317908990866 * q^98 - 45434414156 * q^99

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(45))\)

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
45.12.a	\(\chi_{45}(1, \cdot)\)	45.12.a.a	1	1
		45.12.a.b	1
		45.12.a.c	2
		45.12.a.d	2
		45.12.a.e	2
		45.12.a.f	3
		45.12.a.g	4
		45.12.a.h	4
45.12.b	\(\chi_{45}(19, \cdot)\)	45.12.b.a	2	1
		45.12.b.b	4
		45.12.b.c	8
		45.12.b.d	12
45.12.e	\(\chi_{45}(16, \cdot)\)	45.12.e.a	42	2
		45.12.e.b	46
45.12.f	\(\chi_{45}(8, \cdot)\)	45.12.f.a	44	2
45.12.j	\(\chi_{45}(4, \cdot)\)	45.12.j.a	128	2
45.12.l	\(\chi_{45}(2, \cdot)\)	45.12.l.a	256	4

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(45)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 1}\)