Space of modular forms of level 45 and weight 3

• Label: 45.3
• Level: 45
• Weight: 3
• Dimension: 92
• Nonzero newspaces: 6
• Newform subspaces: 7
• Sturm bound: 432
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 7 \)
Sturm bound:			\(432\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(45))\).

	Total	New	Old
Modular forms	176	120	56
Cusp forms	112	92	20
Eisenstein series	64	28	36

Trace form

92 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 10 * q^5 - 34 * q^6 - 36 * q^8 - 10 * q^9 - 68 * q^10 - 50 * q^11 - 52 * q^12 - 28 * q^13 - 24 * q^14 + 4 * q^15 + 34 * q^16 + 68 * q^17 + 40 * q^18 + 20 * q^19 + 66 * q^20 - 12 * q^21 - 106 * q^22 - 28 * q^23 + 6 * q^24 - 94 * q^25 - 200 * q^26 - 164 * q^27 - 120 * q^28 - 168 * q^29 + 14 * q^30 + 120 * q^31 + 278 * q^32 + 158 * q^33 + 290 * q^34 + 392 * q^35 + 610 * q^36 + 208 * q^37 + 678 * q^38 + 400 * q^39 + 222 * q^40 + 274 * q^41 + 228 * q^42 - 142 * q^43 - 94 * q^45 - 336 * q^46 - 280 * q^47 - 682 * q^48 - 494 * q^49 - 1030 * q^50 - 658 * q^51 - 380 * q^52 - 664 * q^53 - 586 * q^54 + 4 * q^55 - 828 * q^56 - 350 * q^57 + 136 * q^58 - 366 * q^59 - 478 * q^60 - 184 * q^61 - 188 * q^62 - 108 * q^63 + 236 * q^64 + 188 * q^65 + 28 * q^66 + 222 * q^67 + 442 * q^68 + 252 * q^69 + 408 * q^70 + 520 * q^71 + 642 * q^72 + 236 * q^73 + 1044 * q^74 + 1066 * q^75 + 22 * q^76 + 952 * q^77 + 1352 * q^78 - 168 * q^79 + 1280 * q^80 + 938 * q^81 + 76 * q^82 + 908 * q^83 + 1164 * q^84 + 178 * q^85 + 1438 * q^86 + 640 * q^87 + 30 * q^88 - 278 * q^90 + 192 * q^91 - 1048 * q^92 - 972 * q^93 - 412 * q^94 - 1086 * q^95 - 1184 * q^96 - 122 * q^97 - 1688 * q^98 - 1292 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(45))\)

We only show spaces with odd 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
45.3.c	\(\chi_{45}(26, \cdot)\)	45.3.c.a	4	1
45.3.d	\(\chi_{45}(44, \cdot)\)	45.3.d.a	4	1
45.3.g	\(\chi_{45}(28, \cdot)\)	45.3.g.a	4	2
		45.3.g.b	4
45.3.h	\(\chi_{45}(14, \cdot)\)	45.3.h.a	20	2
45.3.i	\(\chi_{45}(11, \cdot)\)	45.3.i.a	16	2
45.3.k	\(\chi_{45}(7, \cdot)\)	45.3.k.a	40	4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces

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