Space of modular forms of level 90 and weight 4

• Label: 90.4
• Level: 90
• Weight: 4
• Dimension: 157
• Nonzero newspaces: 6
• Newform subspaces: 17
• Sturm bound: 1728
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 17 \)
Sturm bound:			\(1728\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(90))\).

	Total	New	Old
Modular forms	712	157	555
Cusp forms	584	157	427
Eisenstein series	128	0	128

Trace form

157 * q - 6 * q^2 - 6 * q^3 + 12 * q^4 - 17 * q^5 + 36 * q^6 + 4 * q^7 + 24 * q^8 + 82 * q^9 - 34 * q^10 - 34 * q^11 + 16 * q^12 + 298 * q^13 + 200 * q^14 + 246 * q^15 + 112 * q^16 + 354 * q^17 - 280 * q^18 - 632 * q^19 - 244 * q^20 - 720 * q^21 - 564 * q^22 - 348 * q^23 + 48 * q^24 + 221 * q^25 + 564 * q^26 + 552 * q^27 + 304 * q^28 + 1878 * q^29 + 288 * q^30 + 948 * q^31 - 96 * q^32 + 286 * q^33 - 824 * q^34 + 128 * q^35 - 584 * q^36 - 2366 * q^37 - 972 * q^38 - 932 * q^39 + 120 * q^40 - 2128 * q^41 - 800 * q^42 + 1222 * q^43 + 640 * q^44 - 2818 * q^45 + 1712 * q^46 - 2148 * q^47 - 224 * q^48 + 303 * q^49 - 734 * q^50 - 30 * q^51 - 440 * q^52 + 954 * q^53 + 300 * q^54 - 248 * q^55 + 544 * q^56 + 4250 * q^57 - 1668 * q^58 + 1298 * q^59 - 152 * q^60 - 5566 * q^61 + 48 * q^62 + 2396 * q^63 - 960 * q^64 - 1068 * q^65 - 480 * q^66 - 4718 * q^67 + 480 * q^68 - 772 * q^69 + 3528 * q^70 + 7968 * q^71 + 48 * q^72 + 1618 * q^73 + 2180 * q^74 + 4740 * q^75 + 4408 * q^76 + 9000 * q^77 + 2216 * q^78 + 7900 * q^79 + 592 * q^80 + 842 * q^81 + 6276 * q^82 - 2292 * q^83 - 1872 * q^84 + 1258 * q^85 - 7484 * q^86 - 8360 * q^87 - 2256 * q^88 - 16454 * q^89 - 6944 * q^90 - 17824 * q^91 - 1392 * q^92 - 5836 * q^93 - 3304 * q^94 + 468 * q^95 - 512 * q^96 + 3196 * q^97 + 438 * q^98 + 2512 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(90))\)

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
90.4.a	\(\chi_{90}(1, \cdot)\)	90.4.a.a	1	1
		90.4.a.b	1
		90.4.a.c	1
		90.4.a.d	1
		90.4.a.e	1
90.4.c	\(\chi_{90}(19, \cdot)\)	90.4.c.a	2	1
		90.4.c.b	2
		90.4.c.c	4
90.4.e	\(\chi_{90}(31, \cdot)\)	90.4.e.a	2	2
		90.4.e.b	4
		90.4.e.c	4
		90.4.e.d	6
		90.4.e.e	8
90.4.f	\(\chi_{90}(17, \cdot)\)	90.4.f.a	4	2
		90.4.f.b	8
90.4.i	\(\chi_{90}(49, \cdot)\)	90.4.i.a	36	2
90.4.l	\(\chi_{90}(23, \cdot)\)	90.4.l.a	72	4

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(90))\) into lower level spaces

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