Space of modular forms of level 18 and weight 16

• Label: 18.16
• Level: 18
• Weight: 16
• Dimension: 36
• Nonzero newspaces: 2
• Newform subspaces: 8
• Sturm bound: 288
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	=	\( 16 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 8 \)
Sturm bound:			\(288\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(18))\).

	Total	New	Old
Modular forms	143	36	107
Cusp forms	127	36	91
Eisenstein series	16	0	16

Trace form

36 * q + 128 * q^2 - 4065 * q^3 - 147456 * q^4 + 410202 * q^5 - 1319040 * q^6 + 5316804 * q^7 - 4194304 * q^8 + 22300923 * q^9 - 43425792 * q^10 + 31054251 * q^11 + 62619648 * q^12 - 171094572 * q^13 + 907519744 * q^14 + 670222170 * q^15 - 2415919104 * q^16 + 7355551602 * q^17 - 4388640000 * q^18 - 11296764918 * q^19 + 6720749568 * q^20 + 2737793988 * q^21 - 33609462912 * q^22 + 42188239752 * q^23 + 8524922880 * q^24 - 12483179253 * q^25 - 199456328192 * q^26 - 165500349552 * q^27 + 166118031360 * q^28 - 231171947052 * q^29 - 223191318528 * q^30 - 507782821230 * q^31 + 34359738368 * q^32 + 671507769033 * q^33 - 229704739200 * q^34 - 3602452563612 * q^35 + 133623791616 * q^36 + 572852437812 * q^37 + 1229694739072 * q^38 - 5130412492254 * q^39 - 711488176128 * q^40 + 6171882883173 * q^41 + 2199962689536 * q^42 - 6640713640611 * q^43 + 1001353543680 * q^44 + 749545049898 * q^45 - 1713647973888 * q^46 - 7555895225868 * q^47 + 65229815808 * q^48 + 4467920151681 * q^49 + 15256648251776 * q^50 - 1708918576029 * q^51 - 2803213467648 * q^52 - 9755568138216 * q^53 + 8219398695552 * q^54 + 42214526191188 * q^55 + 14868803485696 * q^56 + 71516058958023 * q^57 - 30873313476864 * q^58 - 62949177818859 * q^59 - 9008138059776 * q^60 + 6792154341390 * q^61 + 141480239315968 * q^62 - 32066086933218 * q^63 + 158329674399744 * q^64 - 101231408332674 * q^65 + 90166908469248 * q^66 + 102418495674399 * q^67 + 73974991208448 * q^68 - 213939765240426 * q^69 - 26475330465792 * q^70 - 95444171167704 * q^71 - 52563913211904 * q^72 - 381907184866614 * q^73 + 255546837632512 * q^74 - 168864317783109 * q^75 - 34441338765312 * q^76 - 218372475661644 * q^77 + 20008680817920 * q^78 - 183677272321626 * q^79 - 9924595679232 * q^80 - 1152065996686377 * q^81 + 86692609859328 * q^82 - 185009821435578 * q^83 - 373308005646336 * q^84 + 570413595742812 * q^85 + 1144087491247744 * q^86 + 38624745860388 * q^87 - 550657440350208 * q^88 - 2683827880427508 * q^89 - 969227346419712 * q^90 + 2165473654458012 * q^91 + 691212120096768 * q^92 + 1061678246398374 * q^93 - 1244841894837504 * q^94 + 3951482018914584 * q^95 + 214404767416320 * q^96 + 1999117285813485 * q^97 - 3607695794441472 * q^98 - 4878086841309456 * q^99

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(18))\)

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
18.16.a	\(\chi_{18}(1, \cdot)\)	18.16.a.a	1	1
		18.16.a.b	1
		18.16.a.c	1
		18.16.a.d	1
		18.16.a.e	1
		18.16.a.f	1
18.16.c	\(\chi_{18}(7, \cdot)\)	18.16.c.a	14	2
		18.16.c.b	16

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(18)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 1}\)