Space of modular forms of level 45 and weight 8

• Label: 45.8
• Level: 45
• Weight: 8
• Dimension: 351
• Nonzero newspaces: 6
• Newform subspaces: 19
• Sturm bound: 1152
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 19 \)
Sturm bound:			\(1152\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(45))\).

	Total	New	Old
Modular forms	536	377	159
Cusp forms	472	351	121
Eisenstein series	64	26	38

Trace form

351 * q + 32 * q^2 - 56 * q^3 + 82 * q^4 + 591 * q^5 + 2450 * q^6 - 2492 * q^7 - 11184 * q^8 - 6304 * q^9 + 8798 * q^10 + 29708 * q^11 - 2800 * q^12 - 26222 * q^13 - 16452 * q^14 - 24008 * q^15 - 16758 * q^16 + 64934 * q^17 + 16000 * q^18 - 81148 * q^19 - 11132 * q^20 + 199104 * q^21 - 39338 * q^22 + 127068 * q^23 + 4218 * q^24 + 99027 * q^25 - 442540 * q^26 - 747344 * q^27 - 1462200 * q^28 - 371042 * q^29 + 242144 * q^30 + 552768 * q^31 + 3342286 * q^32 + 144356 * q^33 - 127602 * q^34 + 112216 * q^35 - 3210710 * q^36 + 643222 * q^37 - 694954 * q^38 + 63880 * q^39 + 1275036 * q^40 + 3671170 * q^41 + 2293824 * q^42 - 3392792 * q^43 - 5212364 * q^44 + 792872 * q^45 + 1529848 * q^46 + 1352936 * q^47 + 5573786 * q^48 + 2610339 * q^49 - 4019530 * q^50 - 6767872 * q^51 + 3987520 * q^52 + 2505686 * q^53 + 138578 * q^54 - 6575732 * q^55 + 8543244 * q^56 + 5672260 * q^57 - 292200 * q^58 - 8771044 * q^59 - 13935544 * q^60 - 7045806 * q^61 - 20289732 * q^62 + 2912244 * q^63 + 2722060 * q^64 + 26379062 * q^65 + 20517988 * q^66 + 12357040 * q^67 + 36844990 * q^68 + 14326164 * q^69 - 2956662 * q^70 - 22209536 * q^71 - 34627062 * q^72 - 8783390 * q^73 - 52855148 * q^74 + 6965620 * q^75 - 51564634 * q^76 + 2570292 * q^77 + 27934580 * q^78 + 12041420 * q^79 + 47347768 * q^80 + 40947116 * q^81 + 35607232 * q^82 - 15863904 * q^83 - 71092692 * q^84 + 19694318 * q^85 - 13422226 * q^86 + 9776428 * q^87 - 63034602 * q^88 - 6562578 * q^89 + 62362372 * q^90 - 98252752 * q^91 - 11448180 * q^92 - 16333236 * q^93 + 2820228 * q^94 + 19258808 * q^95 - 51487472 * q^96 + 142634266 * q^97 + 122657206 * q^98 + 47668372 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(45))\)

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
45.8.a	\(\chi_{45}(1, \cdot)\)	45.8.a.a	1	1
		45.8.a.b	1
		45.8.a.c	1
		45.8.a.d	1
		45.8.a.e	1
		45.8.a.f	1
		45.8.a.g	1
		45.8.a.h	2
		45.8.a.i	2
45.8.b	\(\chi_{45}(19, \cdot)\)	45.8.b.a	2	1
		45.8.b.b	2
		45.8.b.c	4
		45.8.b.d	8
45.8.e	\(\chi_{45}(16, \cdot)\)	45.8.e.a	26	2
		45.8.e.b	30
45.8.f	\(\chi_{45}(8, \cdot)\)	45.8.f.a	4	2
		45.8.f.b	24
45.8.j	\(\chi_{45}(4, \cdot)\)	45.8.j.a	80	2
45.8.l	\(\chi_{45}(2, \cdot)\)	45.8.l.a	160	4

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(45)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 1}\)