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Properties

Label 18.12
Level 18
Weight 12
Dimension 27
Nonzero newspaces 2
Newform subspaces 7
Sturm bound 216
Trace bound 1

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Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 7 \)
Sturm bound: \(216\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(18))\).

Total New Old
Modular forms 107 27 80
Cusp forms 91 27 64
Eisenstein series 16 0 16

Trace form

\( 27 q + 64 q^{2} - 243 q^{3} - 6144 q^{4} + 10542 q^{5} - 3360 q^{6} - 59706 q^{7} - 32768 q^{8} + 15321 q^{9} + O(q^{10}) \) \( 27 q + 64 q^{2} - 243 q^{3} - 6144 q^{4} + 10542 q^{5} - 3360 q^{6} - 59706 q^{7} - 32768 q^{8} + 15321 q^{9} - 30912 q^{10} + 1332711 q^{11} - 1056768 q^{12} - 1388112 q^{13} + 3059264 q^{14} + 1949040 q^{15} - 6291456 q^{16} - 34245528 q^{17} - 7665216 q^{18} + 31886970 q^{19} + 10795008 q^{20} - 79549062 q^{21} - 22976160 q^{22} + 76016862 q^{23} - 7962624 q^{24} - 138404238 q^{25} + 117846080 q^{26} + 7157808 q^{27} - 8835072 q^{28} + 98644140 q^{29} + 101279232 q^{30} + 24500580 q^{31} + 67108864 q^{32} - 345089835 q^{33} - 269279904 q^{34} + 24476208 q^{35} + 6546432 q^{36} + 224561694 q^{37} + 1176073376 q^{38} + 2177913048 q^{39} - 31653888 q^{40} - 988726209 q^{41} - 786374400 q^{42} + 907703853 q^{43} + 2490292224 q^{44} - 5054109912 q^{45} - 2554368384 q^{46} - 898177794 q^{47} + 1336934400 q^{48} + 3732145806 q^{49} + 5022604096 q^{50} + 2235743865 q^{51} - 1421426688 q^{52} - 20852445738 q^{53} - 6141822048 q^{54} - 3765430872 q^{55} + 3132686336 q^{56} + 16725488049 q^{57} + 3104541696 q^{58} + 21678418305 q^{59} + 1386676224 q^{60} - 15452835402 q^{61} - 50631805696 q^{62} - 43445747676 q^{63} + 28991029248 q^{64} + 63143810916 q^{65} + 21157931520 q^{66} + 11513786415 q^{67} + 4318546944 q^{68} - 23088280320 q^{69} - 12839624832 q^{70} - 50191021536 q^{71} - 14769291264 q^{72} - 42094307700 q^{73} + 19826937152 q^{74} + 208191915321 q^{75} + 34835100672 q^{76} + 135029992914 q^{77} - 84446930880 q^{78} - 105842113620 q^{79} - 14766047232 q^{80} - 226501261803 q^{81} - 2824303488 q^{82} + 98122207512 q^{83} + 118614472704 q^{84} + 236114816292 q^{85} - 5934956512 q^{86} - 44035375302 q^{87} - 23527587840 q^{88} - 485518913322 q^{89} - 196994633472 q^{90} - 273853079496 q^{91} + 77841266688 q^{92} + 503236175280 q^{93} + 134712710208 q^{94} + 442504387824 q^{95} + 11676942336 q^{96} - 379154994837 q^{97} - 464742694944 q^{98} - 705658589190 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(18))\)

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
18.12.a \(\chi_{18}(1, \cdot)\) 18.12.a.a 1 1
18.12.a.b 1
18.12.a.c 1
18.12.a.d 1
18.12.a.e 1
18.12.c \(\chi_{18}(7, \cdot)\) 18.12.c.a 10 2
18.12.c.b 12

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(18)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)