Space of modular forms of level 90 and weight 5

• Label: 90.5
• Level: 90
• Weight: 5
• Dimension: 212
• Nonzero newspaces: 6
• Newform subspaces: 13
• Sturm bound: 2160
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 13 \)
Sturm bound:			\(2160\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(90))\).

	Total	New	Old
Modular forms	928	212	716
Cusp forms	800	212	588
Eisenstein series	128	0	128

Trace form

212 * q - 12 * q^3 - 64 * q^4 - 78 * q^5 - 96 * q^6 + 72 * q^7 + 436 * q^9 - 96 * q^10 + 360 * q^11 - 32 * q^12 - 880 * q^13 - 576 * q^14 - 438 * q^15 + 256 * q^16 + 2580 * q^17 + 2048 * q^18 + 1880 * q^19 + 240 * q^20 - 252 * q^21 - 1952 * q^22 - 7896 * q^23 - 768 * q^24 - 3346 * q^25 - 1344 * q^26 + 192 * q^27 + 672 * q^28 + 3708 * q^29 + 3456 * q^30 + 5556 * q^31 + 1888 * q^33 + 2752 * q^34 + 5196 * q^35 - 1088 * q^36 - 6796 * q^37 - 6816 * q^38 + 7132 * q^39 - 768 * q^40 + 624 * q^41 + 5056 * q^42 - 1924 * q^43 - 10522 * q^45 + 6400 * q^46 - 3408 * q^47 - 2048 * q^48 + 7116 * q^49 - 1536 * q^50 - 4596 * q^51 + 2240 * q^52 - 20580 * q^53 - 17952 * q^54 - 16364 * q^55 + 1536 * q^56 + 8996 * q^57 - 640 * q^58 + 20304 * q^59 + 2032 * q^60 + 41028 * q^61 + 7680 * q^62 + 21668 * q^63 + 8192 * q^64 + 12942 * q^65 + 13632 * q^66 - 26508 * q^67 + 1536 * q^68 - 16612 * q^69 - 36192 * q^70 - 58680 * q^71 - 10752 * q^72 - 60692 * q^73 - 30528 * q^74 - 36534 * q^75 + 13024 * q^76 - 23868 * q^77 - 25792 * q^78 + 31460 * q^79 + 3840 * q^80 + 155756 * q^81 + 46336 * q^82 + 124248 * q^83 + 35520 * q^84 + 32672 * q^85 + 86304 * q^86 + 56380 * q^87 + 15616 * q^88 - 24608 * q^90 - 8576 * q^91 - 63168 * q^92 - 110068 * q^93 - 57664 * q^94 - 193008 * q^95 - 8192 * q^96 - 115372 * q^97 - 88320 * q^98 - 89084 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(90))\)

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
90.5.b	\(\chi_{90}(89, \cdot)\)	90.5.b.a	8	1
90.5.d	\(\chi_{90}(71, \cdot)\)	90.5.d.a	4	1
		90.5.d.b	4
90.5.g	\(\chi_{90}(37, \cdot)\)	90.5.g.a	2	2
		90.5.g.b	2
		90.5.g.c	4
		90.5.g.d	4
		90.5.g.e	4
		90.5.g.f	4
90.5.h	\(\chi_{90}(11, \cdot)\)	90.5.h.a	32	2
90.5.j	\(\chi_{90}(29, \cdot)\)	90.5.j.a	48	2
90.5.k	\(\chi_{90}(7, \cdot)\)	90.5.k.a	48	4
		90.5.k.b	48

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(90))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(90)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)