Space of modular forms of level 45 and weight 2

• Label: 45.2
• Level: 45
• Weight: 2
• Dimension: 39
• Nonzero newspaces: 6
• Newform subspaces: 7
• Sturm bound: 288
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(288\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(45))\).

	Total	New	Old
Modular forms	104	65	39
Cusp forms	41	39	2
Eisenstein series	63	26	37

Trace form

39 * q - 7 * q^2 - 8 * q^3 - 11 * q^4 - 9 * q^5 - 16 * q^6 - 12 * q^7 - 3 * q^8 - 4 * q^9 - 15 * q^10 - 4 * q^11 + 8 * q^12 - 2 * q^13 + 12 * q^14 + 4 * q^15 - 7 * q^16 + 2 * q^17 + 16 * q^18 - 20 * q^19 + 25 * q^20 + 8 * q^22 + 12 * q^23 + 36 * q^24 + 3 * q^25 + 14 * q^26 + 16 * q^27 + 8 * q^28 + 22 * q^29 + 32 * q^30 - 8 * q^31 + 13 * q^32 + 8 * q^33 + 14 * q^34 - 8 * q^35 - 32 * q^36 + 2 * q^37 - 16 * q^38 - 32 * q^39 - 23 * q^40 - 50 * q^41 - 36 * q^42 - 32 * q^43 - 68 * q^44 - 28 * q^45 - 40 * q^46 - 40 * q^47 - 40 * q^48 + 3 * q^49 - 31 * q^50 - 16 * q^51 + 2 * q^52 + 2 * q^53 - 4 * q^54 + 12 * q^55 + 24 * q^56 + 16 * q^57 + 26 * q^58 + 44 * q^59 + 20 * q^60 + 26 * q^61 + 84 * q^62 + 60 * q^63 + 49 * q^64 + 62 * q^65 + 88 * q^66 + 24 * q^67 + 70 * q^68 + 60 * q^69 + 60 * q^70 + 64 * q^71 + 24 * q^72 - 2 * q^73 - 2 * q^74 - 8 * q^75 + 36 * q^76 - 12 * q^77 - 40 * q^78 - 12 * q^79 - 35 * q^80 - 40 * q^81 - 30 * q^82 - 72 * q^83 - 72 * q^84 - 6 * q^85 - 100 * q^86 - 44 * q^87 - 66 * q^89 - 104 * q^90 - 48 * q^91 - 96 * q^92 - 60 * q^93 - 4 * q^94 - 40 * q^95 - 56 * q^96 + 2 * q^97 - 83 * q^98 - 20 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)

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
45.2.a	\(\chi_{45}(1, \cdot)\)	45.2.a.a	1	1
45.2.b	\(\chi_{45}(19, \cdot)\)	45.2.b.a	2	1
45.2.e	\(\chi_{45}(16, \cdot)\)	45.2.e.a	2	2
		45.2.e.b	6
45.2.f	\(\chi_{45}(8, \cdot)\)	45.2.f.a	4	2
45.2.j	\(\chi_{45}(4, \cdot)\)	45.2.j.a	8	2
45.2.l	\(\chi_{45}(2, \cdot)\)	45.2.l.a	16	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces

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