Properties

Label 18.16
Level 18
Weight 16
Dimension 36
Nonzero newspaces 2
Newform subspaces 8
Sturm bound 288
Trace bound 1

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Defining parameters

Level: \( N \) = \( 18 = 2 \cdot 3^{2} \)
Weight: \( k \) = \( 16 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 8 \)
Sturm bound: \(288\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{16}(\Gamma_1(18))\).

Total New Old
Modular forms 143 36 107
Cusp forms 127 36 91
Eisenstein series 16 0 16

Trace form

\( 36 q + 128 q^{2} - 4065 q^{3} - 147456 q^{4} + 410202 q^{5} - 1319040 q^{6} + 5316804 q^{7} - 4194304 q^{8} + 22300923 q^{9} + O(q^{10}) \) \( 36 q + 128 q^{2} - 4065 q^{3} - 147456 q^{4} + 410202 q^{5} - 1319040 q^{6} + 5316804 q^{7} - 4194304 q^{8} + 22300923 q^{9} - 43425792 q^{10} + 31054251 q^{11} + 62619648 q^{12} - 171094572 q^{13} + 907519744 q^{14} + 670222170 q^{15} - 2415919104 q^{16} + 7355551602 q^{17} - 4388640000 q^{18} - 11296764918 q^{19} + 6720749568 q^{20} + 2737793988 q^{21} - 33609462912 q^{22} + 42188239752 q^{23} + 8524922880 q^{24} - 12483179253 q^{25} - 199456328192 q^{26} - 165500349552 q^{27} + 166118031360 q^{28} - 231171947052 q^{29} - 223191318528 q^{30} - 507782821230 q^{31} + 34359738368 q^{32} + 671507769033 q^{33} - 229704739200 q^{34} - 3602452563612 q^{35} + 133623791616 q^{36} + 572852437812 q^{37} + 1229694739072 q^{38} - 5130412492254 q^{39} - 711488176128 q^{40} + 6171882883173 q^{41} + 2199962689536 q^{42} - 6640713640611 q^{43} + 1001353543680 q^{44} + 749545049898 q^{45} - 1713647973888 q^{46} - 7555895225868 q^{47} + 65229815808 q^{48} + 4467920151681 q^{49} + 15256648251776 q^{50} - 1708918576029 q^{51} - 2803213467648 q^{52} - 9755568138216 q^{53} + 8219398695552 q^{54} + 42214526191188 q^{55} + 14868803485696 q^{56} + 71516058958023 q^{57} - 30873313476864 q^{58} - 62949177818859 q^{59} - 9008138059776 q^{60} + 6792154341390 q^{61} + 141480239315968 q^{62} - 32066086933218 q^{63} + 158329674399744 q^{64} - 101231408332674 q^{65} + 90166908469248 q^{66} + 102418495674399 q^{67} + 73974991208448 q^{68} - 213939765240426 q^{69} - 26475330465792 q^{70} - 95444171167704 q^{71} - 52563913211904 q^{72} - 381907184866614 q^{73} + 255546837632512 q^{74} - 168864317783109 q^{75} - 34441338765312 q^{76} - 218372475661644 q^{77} + 20008680817920 q^{78} - 183677272321626 q^{79} - 9924595679232 q^{80} - 1152065996686377 q^{81} + 86692609859328 q^{82} - 185009821435578 q^{83} - 373308005646336 q^{84} + 570413595742812 q^{85} + 1144087491247744 q^{86} + 38624745860388 q^{87} - 550657440350208 q^{88} - 2683827880427508 q^{89} - 969227346419712 q^{90} + 2165473654458012 q^{91} + 691212120096768 q^{92} + 1061678246398374 q^{93} - 1244841894837504 q^{94} + 3951482018914584 q^{95} + 214404767416320 q^{96} + 1999117285813485 q^{97} - 3607695794441472 q^{98} - 4878086841309456 q^{99} + O(q^{100}) \)

Decomposition of \(S_{16}^{\mathrm{new}}(\Gamma_1(18))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
18.16.a \(\chi_{18}(1, \cdot)\) 18.16.a.a 1 1
18.16.a.b 1
18.16.a.c 1
18.16.a.d 1
18.16.a.e 1
18.16.a.f 1
18.16.c \(\chi_{18}(7, \cdot)\) 18.16.c.a 14 2
18.16.c.b 16

Decomposition of \(S_{16}^{\mathrm{old}}(\Gamma_1(18))\) into lower level spaces

\( S_{16}^{\mathrm{old}}(\Gamma_1(18)) \cong \) \(S_{16}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{16}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)