Space of modular forms of level 18 and weight 26

• Label: 18.26
• Level: 18
• Weight: 26
• Dimension: 60
• Nonzero newspaces: 2
• Newform subspaces: 9
• Sturm bound: 468
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	=	\( 26 \)
Nonzero newspaces:			\( 2 \)
Newform subspaces:			\( 9 \)
Sturm bound:			\(468\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{26}(\Gamma_1(18))\).

	Total	New	Old
Modular forms	233	60	173
Cusp forms	217	60	157
Eisenstein series	16	0	16

Trace form

60 * q - 4096 * q^2 + 53637 * q^3 - 251658240 * q^4 - 481593492 * q^5 - 5612752896 * q^6 - 11577984882 * q^7 + 137438953472 * q^8 - 2488574633973 * q^9 + 2866670075904 * q^10 - 20838120149949 * q^11 - 30186909204480 * q^12 + 90383873126778 * q^13 - 230645339070464 * q^14 + 273658932216864 * q^15 - 4222124650659840 * q^16 + 15744805585272894 * q^17 - 3959345703837696 * q^18 + 15933925516712694 * q^19 - 8079798039478272 * q^20 + 57804525572560854 * q^21 - 60870760509591552 * q^22 - 259242792520827594 * q^23 + 17148876699992064 * q^24 - 2064310053322803981 * q^25 + 1664652162118991872 * q^26 - 3935610587588565600 * q^27 - 136441550598045696 * q^28 - 11006204111404564218 * q^29 - 3975133887457394688 * q^30 + 19049515199920964292 * q^31 - 1152921504606846976 * q^32 + 5338811266437199311 * q^33 + 42143618023707389952 * q^34 - 236603264701274086752 * q^35 + 63567605850867499008 * q^36 - 2010250890855963468 * q^37 - 96239735787018973184 * q^38 - 2017291680881948016 * q^39 + 48094743064177803264 * q^40 - 917618093039774692845 * q^41 - 37029197406203412480 * q^42 + 169552080799487032641 * q^43 - 139438906977892171776 * q^44 - 1720188812492486530416 * q^45 + 1032337711883606900736 * q^46 - 1137414750181739218794 * q^47 + 491354822770119671808 * q^48 + 1246203960137256421797 * q^49 - 3592883213612477427712 * q^50 + 2097426154471643578257 * q^51 + 1516389762364549890048 * q^52 - 21368258027703237281916 * q^53 + 3675099065801724039168 * q^54 - 17557531136780454382608 * q^55 - 3869586672978413748224 * q^56 + 11554437912861115739163 * q^57 - 12427984475921336918016 * q^58 + 42821002745218122275661 * q^59 - 30533098614048556056576 * q^60 - 19706043283470126212988 * q^61 + 171134984600668097708032 * q^62 - 74717174009285692495212 * q^63 + 283341988972178712821760 * q^64 + 164597797160174003549256 * q^65 + 269744860212765362749440 * q^66 - 51803926854829943399445 * q^67 - 38638917470405202542592 * q^68 + 9471291412140727885440 * q^69 - 435442230821258493886464 * q^70 + 700180465842066679085496 * q^71 + 46399648582805653291008 * q^72 - 505684575816772825701798 * q^73 - 475494514453868115771392 * q^74 + 644702009291097766007097 * q^75 + 663927720314717205430272 * q^76 - 1765089343549960957945434 * q^77 - 1877655665900919289307136 * q^78 + 1213131573348684356406132 * q^79 - 219752600007888347332608 * q^80 + 2534235254233077966605487 * q^81 - 1788842449372764053102592 * q^82 - 5909739658691180612492532 * q^83 - 432007833378683413856256 * q^84 + 6512081395527007814756520 * q^85 - 1819782369068011588284416 * q^86 - 15564477694869726311501982 * q^87 - 1021241897153687539679232 * q^88 + 27804790231305403802188080 * q^89 - 59120414037307301953536 * q^90 - 14508432146576724633504408 * q^91 - 4349372326565109043298304 * q^92 + 32541372092007723567316320 * q^93 + 1183292281186406977462272 * q^94 - 17974515704961289474235232 * q^95 + 1292139082131132962045952 * q^96 + 9012058602417650348697735 * q^97 + 8025269035314317489577984 * q^98 + 53788802858576975630097234 * q^99

Decomposition of \(S_{26}^{\mathrm{new}}(\Gamma_1(18))\)

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
18.26.a	\(\chi_{18}(1, \cdot)\)	18.26.a.a	1	1
		18.26.a.b	1
		18.26.a.c	1
		18.26.a.d	1
		18.26.a.e	2
		18.26.a.f	2
		18.26.a.g	2
18.26.c	\(\chi_{18}(7, \cdot)\)	18.26.c.a	24	2
		18.26.c.b	26

Decomposition of \(S_{26}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces

\( S_{26}^{\mathrm{old}}(\Gamma_1(18)) \cong \) \(S_{26}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{26}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)