↑

Properties

Label 18.8
Level 18
Weight 8
Dimension 16
Nonzero newspaces 2
Newform subspaces 4
Sturm bound 144
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 8 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 4 \)
Sturm bound: \(144\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(18))\).

Total New Old
Modular forms 71 16 55
Cusp forms 55 16 39
Eisenstein series 16 0 16

Trace form

\( 16 q + 8 q^{2} - 39 q^{3} - 320 q^{4} + 432 q^{5} + 1272 q^{6} - 394 q^{7} - 1024 q^{8} + 57 q^{9} + O(q^{10}) \) \( 16 q + 8 q^{2} - 39 q^{3} - 320 q^{4} + 432 q^{5} + 1272 q^{6} - 394 q^{7} - 1024 q^{8} + 57 q^{9} + 768 q^{10} + 327 q^{11} + 1274 q^{13} + 22768 q^{14} + 18360 q^{15} - 20480 q^{16} - 89862 q^{17} - 3408 q^{18} - 61858 q^{19} + 27648 q^{20} + 277854 q^{21} + 85176 q^{22} - 151842 q^{23} - 7680 q^{24} - 280523 q^{25} - 222368 q^{26} - 200880 q^{27} - 57088 q^{28} + 667110 q^{29} + 456192 q^{30} + 405596 q^{31} + 32768 q^{32} + 517473 q^{33} - 259224 q^{34} - 2547072 q^{35} - 335040 q^{36} - 154636 q^{37} + 394408 q^{38} + 2453976 q^{39} + 49152 q^{40} + 2325933 q^{41} - 403200 q^{42} - 1171507 q^{43} - 1659264 q^{44} - 3451572 q^{45} + 383904 q^{46} + 948462 q^{47} + 159744 q^{48} + 1078083 q^{49} + 1573016 q^{50} - 1970667 q^{51} + 81536 q^{52} + 774492 q^{53} - 581976 q^{54} + 456768 q^{55} + 1457152 q^{56} + 1182801 q^{57} + 141552 q^{58} - 500151 q^{59} - 2059776 q^{60} + 3324992 q^{61} - 789056 q^{62} - 4404036 q^{63} + 4194304 q^{64} - 2256444 q^{65} - 4022784 q^{66} - 9945385 q^{67} + 2097984 q^{68} + 9507348 q^{69} + 1523328 q^{70} + 6938328 q^{71} + 2320896 q^{72} + 16973366 q^{73} + 6224224 q^{74} - 22090299 q^{75} + 531776 q^{76} - 1656498 q^{77} - 6015408 q^{78} - 9991828 q^{79} + 442368 q^{80} + 11656701 q^{81} - 12819984 q^{82} - 30336996 q^{83} - 8969856 q^{84} + 603072 q^{85} - 5519384 q^{86} + 25741386 q^{87} + 5451264 q^{88} + 55826400 q^{89} + 46925568 q^{90} - 3542552 q^{91} - 9717888 q^{92} - 17811900 q^{93} - 13044048 q^{94} - 53912736 q^{95} - 4718592 q^{96} - 16861735 q^{97} - 39695568 q^{98} + 15105546 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(18))\)

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
18.8.a \(\chi_{18}(1, \cdot)\) 18.8.a.a 1 1
18.8.a.b 1
18.8.c \(\chi_{18}(7, \cdot)\) 18.8.c.a 6 2
18.8.c.b 8

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(18)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 1}\)