Space of modular forms of level 45 and weight 5

• Label: 45.5
• Level: 45
• Weight: 5
• Dimension: 194
• Nonzero newspaces: 6
• Newform subspaces: 10
• Sturm bound: 720
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(720\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(45))\).

	Total	New	Old
Modular forms	320	222	98
Cusp forms	256	194	62
Eisenstein series	64	28	36

Trace form

194 * q - 2 * q^3 - 26 * q^4 + 48 * q^5 + 182 * q^6 + 32 * q^7 - 192 * q^8 - 346 * q^9 + 14 * q^10 - 366 * q^11 - 28 * q^12 + 1134 * q^13 + 2280 * q^14 + 670 * q^15 - 1022 * q^16 - 1806 * q^17 - 4160 * q^18 - 2780 * q^19 - 4014 * q^20 - 1992 * q^21 + 2478 * q^22 + 4668 * q^23 + 7134 * q^24 + 6110 * q^25 + 7692 * q^26 + 2284 * q^27 - 192 * q^28 + 2100 * q^29 - 1090 * q^30 - 3700 * q^31 - 8442 * q^32 - 526 * q^33 - 18862 * q^34 - 8868 * q^35 - 3470 * q^36 + 4402 * q^37 - 1434 * q^38 - 11036 * q^39 + 16258 * q^40 - 10242 * q^41 - 24612 * q^42 - 2070 * q^43 + 5264 * q^45 + 1224 * q^46 + 10128 * q^47 + 31694 * q^48 + 3390 * q^49 + 21912 * q^50 + 16670 * q^51 + 18808 * q^52 + 31434 * q^53 + 26222 * q^54 + 23608 * q^55 + 25332 * q^56 - 17342 * q^57 - 10792 * q^58 - 31722 * q^59 - 42010 * q^60 - 49212 * q^61 - 53940 * q^62 - 4872 * q^63 - 46532 * q^64 - 19620 * q^65 + 21028 * q^66 + 10190 * q^67 + 27990 * q^68 + 28368 * q^69 + 25200 * q^70 + 21312 * q^71 + 44538 * q^72 + 25374 * q^73 + 44100 * q^74 + 22876 * q^75 + 8142 * q^76 - 17220 * q^77 - 33208 * q^78 + 9492 * q^79 - 129600 * q^80 - 118606 * q^81 - 20540 * q^82 - 59004 * q^83 - 132516 * q^84 + 10160 * q^85 - 41682 * q^86 - 9164 * q^87 - 54522 * q^88 + 28426 * q^90 - 44480 * q^91 + 101880 * q^92 + 60408 * q^93 - 5644 * q^94 + 102702 * q^95 + 219184 * q^96 + 58588 * q^97 + 149382 * q^98 + 98080 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(45))\)

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
45.5.c	\(\chi_{45}(26, \cdot)\)	45.5.c.a	4	1
45.5.d	\(\chi_{45}(44, \cdot)\)	45.5.d.a	8	1
45.5.g	\(\chi_{45}(28, \cdot)\)	45.5.g.a	2	2
		45.5.g.b	2
		45.5.g.c	2
		45.5.g.d	4
		45.5.g.e	8
45.5.h	\(\chi_{45}(14, \cdot)\)	45.5.h.a	44	2
45.5.i	\(\chi_{45}(11, \cdot)\)	45.5.i.a	32	2
45.5.k	\(\chi_{45}(7, \cdot)\)	45.5.k.a	88	4

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(45))\) into lower level spaces

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