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Properties

Label 18.6
Level 18
Weight 6
Dimension 13
Nonzero newspaces 2
Newform subspaces 5
Sturm bound 108
Trace bound 1

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Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 5 \)
Sturm bound: \(108\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(18))\).

Total New Old
Modular forms 53 13 40
Cusp forms 37 13 24
Eisenstein series 16 0 16

Trace form

\( 13 q - 8 q^{2} + 9 q^{3} - 32 q^{4} - 42 q^{5} - 84 q^{6} - 178 q^{7} + 64 q^{8} + 579 q^{9} + O(q^{10}) \) \( 13 q - 8 q^{2} + 9 q^{3} - 32 q^{4} - 42 q^{5} - 84 q^{6} - 178 q^{7} + 64 q^{8} + 579 q^{9} + 504 q^{10} - 333 q^{11} - 384 q^{12} - 964 q^{13} - 1528 q^{14} + 2664 q^{15} - 512 q^{16} + 4296 q^{17} + 2568 q^{18} - 1390 q^{19} - 672 q^{20} - 11310 q^{21} - 4260 q^{22} - 9306 q^{23} + 576 q^{24} + 13594 q^{25} + 17432 q^{26} + 18144 q^{27} - 64 q^{28} - 14616 q^{29} - 7488 q^{30} - 16612 q^{31} - 2048 q^{32} - 405 q^{33} - 10092 q^{34} + 12048 q^{35} - 7440 q^{36} + 33482 q^{37} - 14908 q^{38} - 30432 q^{39} + 8064 q^{40} + 1209 q^{41} + 36960 q^{42} - 14959 q^{43} + 13536 q^{44} + 7884 q^{45} + 14160 q^{46} + 57558 q^{47} + 3840 q^{48} + 1950 q^{49} - 28712 q^{50} - 44379 q^{51} - 15424 q^{52} - 97446 q^{53} - 116604 q^{54} - 13608 q^{55} - 24448 q^{56} + 89667 q^{57} + 16512 q^{58} + 58581 q^{59} + 42624 q^{60} - 18442 q^{61} + 120992 q^{62} + 55788 q^{63} + 53248 q^{64} + 77856 q^{65} + 80064 q^{66} + 60275 q^{67} - 24432 q^{68} - 68292 q^{69} - 170064 q^{70} - 283488 q^{71} - 59712 q^{72} - 170020 q^{73} - 65224 q^{74} - 86403 q^{75} + 2192 q^{76} + 120762 q^{77} + 240840 q^{78} + 204836 q^{79} + 72192 q^{80} + 173007 q^{81} + 212976 q^{82} + 129864 q^{83} - 2016 q^{84} - 106380 q^{85} - 310252 q^{86} - 170046 q^{87} - 68160 q^{88} + 80274 q^{89} - 344736 q^{90} - 219656 q^{91} - 148896 q^{92} - 87780 q^{93} + 26760 q^{94} + 131568 q^{95} + 12288 q^{96} + 122189 q^{97} + 609732 q^{98} + 601794 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)

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
18.6.a \(\chi_{18}(1, \cdot)\) 18.6.a.a 1 1
18.6.a.b 1
18.6.a.c 1
18.6.c \(\chi_{18}(7, \cdot)\) 18.6.c.a 4 2
18.6.c.b 6

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces

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