Space of modular forms of level 90 and weight 3

• Label: 90.3
• Level: 90
• Weight: 3
• Dimension: 102
• Nonzero newspaces: 5
• Newform subspaces: 10
• Sturm bound: 1296
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 5 \)
Newform subspaces:			\( 10 \)
Sturm bound:			\(1296\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(90))\).

	Total	New	Old
Modular forms	496	102	394
Cusp forms	368	102	266
Eisenstein series	128	0	128

Trace form

102 * q - 2 * q^2 + 18 * q^5 + 24 * q^6 + 16 * q^7 + 4 * q^8 + 16 * q^9 + 42 * q^10 + 44 * q^11 - 8 * q^12 + 26 * q^13 - 72 * q^14 - 42 * q^15 - 8 * q^16 - 130 * q^17 - 16 * q^18 - 16 * q^19 - 40 * q^20 + 36 * q^21 + 8 * q^22 + 8 * q^23 + 60 * q^25 - 12 * q^26 + 48 * q^27 - 56 * q^28 - 36 * q^29 - 72 * q^30 - 212 * q^31 + 8 * q^32 - 380 * q^33 - 40 * q^34 - 484 * q^35 - 152 * q^36 - 46 * q^37 - 40 * q^38 - 356 * q^39 + 36 * q^40 - 52 * q^41 - 32 * q^42 + 200 * q^43 + 134 * q^45 - 136 * q^46 + 168 * q^47 + 16 * q^48 + 156 * q^49 + 242 * q^50 + 720 * q^51 - 28 * q^52 + 562 * q^53 + 408 * q^54 - 436 * q^55 - 32 * q^56 + 368 * q^57 - 56 * q^58 + 108 * q^59 + 148 * q^60 + 412 * q^61 + 472 * q^62 - 100 * q^63 + 96 * q^64 + 408 * q^65 + 528 * q^66 + 496 * q^67 + 116 * q^68 + 164 * q^69 + 372 * q^70 + 40 * q^71 + 192 * q^72 + 354 * q^73 - 144 * q^74 - 1002 * q^75 - 96 * q^76 - 620 * q^77 - 448 * q^78 + 356 * q^79 - 568 * q^81 - 520 * q^82 - 456 * q^83 + 48 * q^84 - 410 * q^85 - 480 * q^86 - 164 * q^87 - 16 * q^88 + 64 * q^90 - 992 * q^91 + 16 * q^92 + 404 * q^93 - 8 * q^94 + 1012 * q^95 - 32 * q^96 - 634 * q^97 + 494 * q^98 + 868 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(90))\)

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
90.3.b	\(\chi_{90}(89, \cdot)\)	90.3.b.a	4	1
90.3.d	\(\chi_{90}(71, \cdot)\)	None	0	1
90.3.g	\(\chi_{90}(37, \cdot)\)	90.3.g.a	2	2
		90.3.g.b	2
		90.3.g.c	2
		90.3.g.d	4
90.3.h	\(\chi_{90}(11, \cdot)\)	90.3.h.a	16	2
90.3.j	\(\chi_{90}(29, \cdot)\)	90.3.j.a	8	2
		90.3.j.b	16
90.3.k	\(\chi_{90}(7, \cdot)\)	90.3.k.a	24	4
		90.3.k.b	24

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(90))\) into lower level spaces

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