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Properties

Label 54.11
Level 54
Weight 11
Dimension 214
Nonzero newspaces 3
Newform subspaces 5
Sturm bound 1782
Trace bound 1

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Defining parameters

Level: \( N \) = \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 5 \)
Sturm bound: \(1782\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(54))\).

Total New Old
Modular forms 840 214 626
Cusp forms 780 214 566
Eisenstein series 60 0 60

Trace form

\( 214 q - 2048 q^{4} + 19836 q^{5} - 18240 q^{6} + 28316 q^{7} - 238260 q^{9} + O(q^{10}) \) \( 214 q - 2048 q^{4} + 19836 q^{5} - 18240 q^{6} + 28316 q^{7} - 238260 q^{9} - 23424 q^{10} + 655164 q^{11} + 33792 q^{12} - 1990732 q^{13} - 351360 q^{14} + 3865842 q^{15} + 1048576 q^{16} + 2035968 q^{18} - 6137146 q^{19} - 5078016 q^{20} + 30440868 q^{21} - 6163200 q^{22} - 17879850 q^{23} + 44908 q^{25} + 86086422 q^{27} + 4299776 q^{28} + 2244546 q^{29} - 96350976 q^{30} + 82537904 q^{31} + 132349248 q^{33} - 111857280 q^{34} + 520307226 q^{35} - 21596160 q^{36} - 106979398 q^{37} - 370117440 q^{38} - 370412790 q^{39} + 11993088 q^{40} + 876008916 q^{41} + 489739008 q^{42} + 466787120 q^{43} - 901730718 q^{45} - 545013504 q^{46} - 214514136 q^{47} - 48758784 q^{48} + 406505664 q^{49} + 913213440 q^{50} + 6536862 q^{51} + 1019254784 q^{52} - 2105146944 q^{54} - 4251178044 q^{55} - 179896320 q^{56} + 2731065300 q^{57} + 2001384576 q^{58} - 621945450 q^{59} + 1753168896 q^{60} + 4567725500 q^{61} - 163672062 q^{63} + 7516192768 q^{64} - 8022433032 q^{65} + 3649473792 q^{66} + 285966650 q^{67} + 3007226880 q^{68} + 1508853546 q^{69} + 3052836672 q^{70} + 11025824328 q^{71} + 6086197248 q^{72} - 12484826356 q^{73} - 10143019008 q^{74} - 13544183778 q^{75} - 3093369856 q^{76} + 22761221436 q^{77} - 5578154496 q^{78} - 17957753128 q^{79} - 1264415508 q^{81} - 1967124480 q^{82} - 2027184732 q^{83} + 10216212480 q^{84} + 39341692620 q^{85} + 17155276416 q^{86} - 21225460878 q^{87} - 12850200576 q^{88} - 60289063668 q^{89} - 42769647360 q^{90} - 40827946364 q^{91} + 3805820928 q^{92} + 17976874674 q^{93} + 73048572480 q^{94} + 88198956792 q^{95} - 1107296256 q^{96} - 24295490578 q^{97} - 72176531328 q^{98} + 22964705082 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(54))\)

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
54.11.b \(\chi_{54}(53, \cdot)\) 54.11.b.a 2 1
54.11.b.b 4
54.11.b.c 8
54.11.d \(\chi_{54}(17, \cdot)\) 54.11.d.a 20 2
54.11.f \(\chi_{54}(5, \cdot)\) 54.11.f.a 180 6

Decomposition of \(S_{11}^{\mathrm{old}}(\Gamma_1(54))\) into lower level spaces

\( S_{11}^{\mathrm{old}}(\Gamma_1(54)) \cong \) \(S_{11}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{11}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)