Space of modular forms of level 90 and weight 2

• Label: 90.2
• Level: 90
• Weight: 2
• Dimension: 53
• Nonzero newspaces: 6
• Newform subspaces: 12
• Sturm bound: 864
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 12 \)
Sturm bound:			\(864\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(90))\).

	Total	New	Old
Modular forms	280	53	227
Cusp forms	153	53	100
Eisenstein series	127	0	127

Trace form

53 * q + 3 * q^2 + 6 * q^3 + 3 * q^4 + 5 * q^5 - 6 * q^6 + 12 * q^7 - 3 * q^8 - 14 * q^9 - 11 * q^10 - 26 * q^11 - 8 * q^12 - 14 * q^13 - 20 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 4 * q^18 - 8 * q^19 - 11 * q^20 - 36 * q^21 - 10 * q^22 - 36 * q^23 + 6 * q^24 - 17 * q^25 + 6 * q^26 - 24 * q^27 - 6 * q^29 - 8 * q^31 + 3 * q^32 + 10 * q^33 + 4 * q^34 + 16 * q^35 + 10 * q^36 - 26 * q^37 + 42 * q^38 + 64 * q^39 - 3 * q^40 + 76 * q^41 + 64 * q^42 + 10 * q^43 + 32 * q^44 + 80 * q^45 + 60 * q^47 + 10 * q^48 + 3 * q^49 + 47 * q^50 + 30 * q^51 + 10 * q^52 + 30 * q^53 + 30 * q^54 - 20 * q^55 + 20 * q^56 + 26 * q^57 + 34 * q^58 + 10 * q^59 - 8 * q^60 + 14 * q^61 - 40 * q^63 - 3 * q^64 - 42 * q^65 - 48 * q^66 - 18 * q^67 - 36 * q^68 - 64 * q^69 - 24 * q^70 - 72 * q^71 - 6 * q^72 - 58 * q^73 - 50 * q^74 + 6 * q^75 - 46 * q^76 - 12 * q^77 - 28 * q^78 - 32 * q^79 + 5 * q^80 + 2 * q^81 - 58 * q^82 + 36 * q^83 - 12 * q^84 - 30 * q^85 - 70 * q^86 - 20 * q^87 - 10 * q^88 - 46 * q^89 - 56 * q^90 - 64 * q^91 - 36 * q^92 + 32 * q^93 - 28 * q^94 + 12 * q^95 - 8 * q^96 - 44 * q^97 - 27 * q^98 - 20 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)

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
90.2.a	\(\chi_{90}(1, \cdot)\)	90.2.a.a	1	1
		90.2.a.b	1
		90.2.a.c	1
90.2.c	\(\chi_{90}(19, \cdot)\)	90.2.c.a	2	1
90.2.e	\(\chi_{90}(31, \cdot)\)	90.2.e.a	2	2
		90.2.e.b	2
		90.2.e.c	4
90.2.f	\(\chi_{90}(17, \cdot)\)	90.2.f.a	4	2
90.2.i	\(\chi_{90}(49, \cdot)\)	90.2.i.a	4	2
		90.2.i.b	8
90.2.l	\(\chi_{90}(23, \cdot)\)	90.2.l.a	8	4
		90.2.l.b	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(90))\) into lower level spaces

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