Space of modular forms of level 90 and weight 18

• Label: 90.18
• Level: 90
• Weight: 18
• Dimension: 885
• Nonzero newspaces: 6
• Sturm bound: 7776
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 90 = 2 \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	=	\( 18 \)
Nonzero newspaces:			\( 6 \)
Sturm bound:			\(7776\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(90))\).

	Total	New	Old
Modular forms	3736	885	2851
Cusp forms	3608	885	2723
Eisenstein series	128	0	128

Trace form

885 * q + 768 * q^2 - 954 * q^3 + 1245184 * q^4 + 997457 * q^5 - 14550528 * q^6 + 21245772 * q^7 - 50331648 * q^8 + 1134224890 * q^9 - 1026886400 * q^10 + 3212251078 * q^11 + 597164032 * q^12 + 227537786 * q^13 - 10125464576 * q^14 + 15406493232 * q^15 + 150323855360 * q^16 - 34065415938 * q^17 + 55077764096 * q^18 + 174902671352 * q^19 - 325095194624 * q^20 + 694017551124 * q^21 - 1429407173120 * q^22 - 589561135716 * q^23 - 16005464064 * q^24 - 7855616191621 * q^25 - 7183633119744 * q^26 + 12715299827976 * q^27 + 5990268272640 * q^28 - 24625678270734 * q^29 - 9158521946112 * q^30 + 52140233085736 * q^31 + 3298534883328 * q^32 - 32146388461910 * q^33 - 9978769996800 * q^34 - 21236345169872 * q^35 + 33928294039552 * q^36 - 73346511268186 * q^37 - 23823892796928 * q^38 + 156393107888944 * q^39 - 5466469957632 * q^40 + 211800197395324 * q^41 - 248456112521216 * q^42 - 24713721892630 * q^43 + 210508634390528 * q^44 + 64491437763836 * q^45 + 273815818747904 * q^46 - 662552616081060 * q^47 + 26843545600000 * q^48 - 277875888634725 * q^49 + 1317128274063104 * q^50 + 3740273067539646 * q^51 - 784982602547200 * q^52 - 6296175419779650 * q^53 + 2837214067072512 * q^54 + 4085901699640188 * q^55 - 725129730457600 * q^56 - 1889450727181534 * q^57 - 1294052181024256 * q^58 - 3978925336566902 * q^59 - 892727330865152 * q^60 + 14827526797106870 * q^61 + 432728671764480 * q^62 - 14818733709535000 * q^63 - 23362423066984448 * q^64 + 11191035763077762 * q^65 + 12114179437940736 * q^66 + 8255603805174222 * q^67 - 10034551481696256 * q^68 - 32825406554575720 * q^69 - 3906834893322240 * q^70 + 152545121019332376 * q^71 + 398433277968384 * q^72 - 46838652179873978 * q^73 - 16244812661109248 * q^74 - 72047318281033386 * q^75 + 12689175452188672 * q^76 + 126818720202776268 * q^77 - 54910262991920128 * q^78 - 48770698571132944 * q^79 + 7761577134522368 * q^80 - 29951732170941382 * q^81 - 27553561893452288 * q^82 + 181170462300565956 * q^83 + 95634219324407808 * q^84 + 219685488701268730 * q^85 - 82856828455912960 * q^86 - 441809156435744900 * q^87 - 93677628497592320 * q^88 + 551590761608405762 * q^89 + 15809429672888320 * q^90 + 54791046178022272 * q^91 - 38637478590283776 * q^92 - 99405709205524408 * q^93 + 3900652257911808 * q^94 + 288626208050116524 * q^95 + 22579570788007936 * q^96 - 546983382247601644 * q^97 - 579969774924110592 * q^98 - 215507910042658868 * q^99

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(90))\)

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
90.18.a	\(\chi_{90}(1, \cdot)\)	90.18.a.a	1	1
		90.18.a.b	1
		90.18.a.c	1
		90.18.a.d	1
		90.18.a.e	1
		90.18.a.f	1
		90.18.a.g	1
		90.18.a.h	2
		90.18.a.i	2
		90.18.a.j	2
		90.18.a.k	2
		90.18.a.l	2
		90.18.a.m	2
		90.18.a.n	2
		90.18.a.o	3
		90.18.a.p	3
90.18.c	\(\chi_{90}(19, \cdot)\)	90.18.c.a	8	1
		90.18.c.b	8
		90.18.c.c	10
		90.18.c.d	16
90.18.e	\(\chi_{90}(31, \cdot)\)	n/a	136	2
90.18.f	\(\chi_{90}(17, \cdot)\)	90.18.f.a	32	2
		90.18.f.b	36
90.18.i	\(\chi_{90}(49, \cdot)\)	n/a	204	2
90.18.l	\(\chi_{90}(23, \cdot)\)	n/a	408	4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(90))\) into lower level spaces

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