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Properties

Label 63.18
Level 63
Weight 18
Dimension 1835
Nonzero newspaces 10
Sturm bound 5184
Trace bound 2

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Defining parameters

Level: \( N \) = \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) = \( 18 \)
Nonzero newspaces: \( 10 \)
Sturm bound: \(5184\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(63))\).

Total New Old
Modular forms 2496 1879 617
Cusp forms 2400 1835 565
Eisenstein series 96 44 52

Trace form

\( 1835 q + 21 q^{2} + 4548 q^{3} + 1758801 q^{4} - 1198806 q^{5} + 23947782 q^{6} + 22774527 q^{7} + 385854783 q^{8} - 722836056 q^{9} + O(q^{10}) \) \( 1835 q + 21 q^{2} + 4548 q^{3} + 1758801 q^{4} - 1198806 q^{5} + 23947782 q^{6} + 22774527 q^{7} + 385854783 q^{8} - 722836056 q^{9} + 815312550 q^{10} - 3021924282 q^{11} + 2085977580 q^{12} - 7981267576 q^{13} - 43779459717 q^{14} + 65112235260 q^{15} - 79198340083 q^{16} + 53284955142 q^{17} - 139911765108 q^{18} - 213483142984 q^{19} + 992352629022 q^{20} - 198889154700 q^{21} + 900585561210 q^{22} - 546389014254 q^{23} + 4088294151306 q^{24} + 2308330604171 q^{25} + 6849922721574 q^{26} - 3565630711434 q^{27} - 6200969128303 q^{28} - 4791703517502 q^{29} + 22588660813890 q^{30} + 13005045233186 q^{31} - 20002261697961 q^{32} - 59438982574788 q^{33} - 20343952640922 q^{34} - 88521282143232 q^{35} + 131765899729518 q^{36} + 125993599609056 q^{37} - 360853633647516 q^{38} + 93975117194592 q^{39} + 185135804638674 q^{40} + 232786960761324 q^{41} - 355651496134416 q^{42} - 756945093044328 q^{43} + 534043079969694 q^{44} + 770690638020600 q^{45} + 994519668087102 q^{46} - 1155380250160842 q^{47} + 928029009661866 q^{48} - 2683056919535683 q^{49} + 206560789831479 q^{50} + 630876715648980 q^{51} + 942783558611498 q^{52} - 1201389051747192 q^{53} + 11697873652777404 q^{54} - 5721173586700056 q^{55} - 6048976597520625 q^{56} - 400083899741772 q^{57} - 518669799342396 q^{58} + 2441365548710472 q^{59} + 9316824138681150 q^{60} - 134186180897380 q^{61} + 5044456098985044 q^{62} - 12695728466324796 q^{63} - 6420052187151795 q^{64} + 20631167616769644 q^{65} - 3744973850645358 q^{66} + 306061766273188 q^{67} + 18828585328823610 q^{68} - 24031519550266464 q^{69} - 106221997918870350 q^{70} + 3334332449625396 q^{71} + 97402382562362064 q^{72} + 57775750258420904 q^{73} - 120959729120367990 q^{74} - 90010584241645296 q^{75} - 16744798761947230 q^{76} + 113408028034245156 q^{77} + 65309792366773272 q^{78} - 31828528015082384 q^{79} - 315676697359579986 q^{80} - 132575457655687860 q^{81} + 16594588275273978 q^{82} + 212736668571572946 q^{83} + 63148790613352638 q^{84} - 145398302375813484 q^{85} - 283683169280031384 q^{86} + 18647414617262478 q^{87} - 26684639236637772 q^{88} - 243817156854000858 q^{89} + 894962386590165114 q^{90} + 296391815862470678 q^{91} + 501712410065247552 q^{92} - 620478730954113258 q^{93} - 749693684527408548 q^{94} - 120833599152625722 q^{95} + 883473561876636168 q^{96} + 355604273783733296 q^{97} - 266372508549358737 q^{98} - 608883641823678696 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(63))\)

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
63.18.a \(\chi_{63}(1, \cdot)\) 63.18.a.a 3 1
63.18.a.b 4
63.18.a.c 4
63.18.a.d 4
63.18.a.e 5
63.18.a.f 5
63.18.a.g 8
63.18.a.h 10
63.18.c \(\chi_{63}(62, \cdot)\) 63.18.c.a 4 1
63.18.c.b 40
63.18.e \(\chi_{63}(37, \cdot)\) n/a 112 2
63.18.f \(\chi_{63}(22, \cdot)\) n/a 204 2
63.18.g \(\chi_{63}(4, \cdot)\) n/a 268 2
63.18.h \(\chi_{63}(25, \cdot)\) n/a 268 2
63.18.i \(\chi_{63}(5, \cdot)\) n/a 268 2
63.18.o \(\chi_{63}(20, \cdot)\) n/a 268 2
63.18.p \(\chi_{63}(17, \cdot)\) 63.18.p.a 92 2
63.18.s \(\chi_{63}(47, \cdot)\) n/a 268 2

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(63))\) into lower level spaces

\( S_{18}^{\mathrm{old}}(\Gamma_1(63)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 1}\)