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Properties

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

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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

\( 60 q - 4096 q^{2} + 53637 q^{3} - 251658240 q^{4} - 481593492 q^{5} - 5612752896 q^{6} - 11577984882 q^{7} + 137438953472 q^{8} - 2488574633973 q^{9} + O(q^{10}) \) \( 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} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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