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Properties

Label 18.7
Level 18
Weight 7
Dimension 14
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 126
Trace bound 1

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Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(126\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(18))\).

Total New Old
Modular forms 62 14 48
Cusp forms 46 14 32
Eisenstein series 16 0 16

Trace form

\( 14 q - 42 q^{3} + 128 q^{4} + 432 q^{5} - 144 q^{6} - 728 q^{7} + 2190 q^{9} + O(q^{10}) \) \( 14 q - 42 q^{3} + 128 q^{4} + 432 q^{5} - 144 q^{6} - 728 q^{7} + 2190 q^{9} - 1968 q^{10} + 378 q^{11} + 384 q^{12} + 8416 q^{13} - 4752 q^{14} - 10872 q^{15} - 4096 q^{16} - 2976 q^{18} + 8668 q^{19} + 13824 q^{20} + 24876 q^{21} - 18768 q^{22} - 76248 q^{23} - 6144 q^{24} - 21172 q^{25} + 127008 q^{27} + 46336 q^{28} + 97092 q^{29} + 34272 q^{30} - 58112 q^{31} - 246258 q^{33} - 27504 q^{34} + 38208 q^{36} + 79516 q^{37} + 97632 q^{38} + 42204 q^{39} + 62976 q^{40} - 410562 q^{41} - 222144 q^{42} + 79030 q^{43} + 13716 q^{45} - 96864 q^{46} + 347652 q^{47} + 55296 q^{48} + 97260 q^{49} + 311040 q^{50} + 336402 q^{51} - 269312 q^{52} - 173520 q^{54} + 113976 q^{55} - 152064 q^{56} - 522282 q^{57} - 172848 q^{58} + 369738 q^{59} - 170496 q^{60} + 162244 q^{61} - 103800 q^{63} - 458752 q^{64} - 753840 q^{65} + 909216 q^{66} + 47998 q^{67} + 744768 q^{68} + 2059272 q^{69} + 1108464 q^{70} - 374784 q^{72} - 505412 q^{73} - 2197152 q^{74} - 2115342 q^{75} - 412736 q^{76} - 159192 q^{77} - 631488 q^{78} - 835028 q^{79} - 1428282 q^{81} + 1492176 q^{82} + 396900 q^{83} + 1441536 q^{84} + 1615140 q^{85} + 3264624 q^{86} + 3072636 q^{87} + 600576 q^{88} - 1987200 q^{90} - 2904640 q^{91} - 2439936 q^{92} - 2526576 q^{93} - 1605648 q^{94} - 2089260 q^{95} - 49152 q^{96} - 681722 q^{97} + 4398804 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(18))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
18.7.b \(\chi_{18}(17, \cdot)\) 18.7.b.a 2 1
18.7.d \(\chi_{18}(5, \cdot)\) 18.7.d.a 12 2

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(18)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 1}\)