Properties

Label 18.9
Level 18
Weight 9
Dimension 20
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 162
Trace bound 1

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Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 9 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(162\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(\Gamma_1(18))\).

Total New Old
Modular forms 80 20 60
Cusp forms 64 20 44
Eisenstein series 16 0 16

Trace form

\( 20 q + 126 q^{3} + 512 q^{4} - 882 q^{5} + 384 q^{6} - 5606 q^{7} - 28662 q^{9} + O(q^{10}) \) \( 20 q + 126 q^{3} + 512 q^{4} - 882 q^{5} + 384 q^{6} - 5606 q^{7} - 28662 q^{9} + 15360 q^{10} + 45756 q^{11} + 5376 q^{12} + 5590 q^{13} - 94464 q^{14} + 128754 q^{15} - 65536 q^{16} - 236544 q^{18} - 197756 q^{19} - 112896 q^{20} - 299166 q^{21} + 706176 q^{22} + 1311138 q^{23} - 147456 q^{24} + 752894 q^{25} - 208656 q^{27} + 8704 q^{28} - 2851290 q^{29} - 1253376 q^{30} + 368374 q^{31} + 3875796 q^{33} + 570624 q^{34} - 3655680 q^{36} - 1677512 q^{37} - 1314432 q^{38} - 5896002 q^{39} - 1966080 q^{40} + 9218592 q^{41} + 14237952 q^{42} + 18255832 q^{43} - 32740578 q^{45} - 5184000 q^{46} - 34980606 q^{47} - 1376256 q^{48} + 4984398 q^{49} + 27744768 q^{50} + 50877810 q^{51} - 715520 q^{52} - 5648256 q^{54} - 20275956 q^{55} - 12091392 q^{56} - 34049898 q^{57} - 7038720 q^{58} + 93924216 q^{59} + 18604800 q^{60} - 7052474 q^{61} - 14043234 q^{63} - 41943040 q^{64} - 126568134 q^{65} - 35179776 q^{66} + 79052404 q^{67} - 5476608 q^{68} + 70499610 q^{69} + 18386688 q^{70} - 11894784 q^{72} - 128649524 q^{73} + 35124480 q^{74} + 114494910 q^{75} + 94851328 q^{76} + 9309294 q^{77} + 23014656 q^{78} + 45212026 q^{79} - 46018134 q^{81} - 121340928 q^{82} + 114200226 q^{83} - 15040512 q^{84} - 371086812 q^{85} - 171379584 q^{86} - 159599970 q^{87} - 90390528 q^{88} + 129745152 q^{90} + 717011468 q^{91} + 167825664 q^{92} + 120711534 q^{93} - 21755136 q^{94} - 143949240 q^{95} - 25165824 q^{96} - 151743164 q^{97} + 366888330 q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(\Gamma_1(18))\)

We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
18.9.b \(\chi_{18}(17, \cdot)\) 18.9.b.a 2 1
18.9.b.b 2
18.9.d \(\chi_{18}(5, \cdot)\) 18.9.d.a 16 2

Decomposition of \(S_{9}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces

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