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Properties

Label 54.10
Level 54
Weight 10
Dimension 192
Nonzero newspaces 3
Newform subspaces 12
Sturm bound 1620
Trace bound 1

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Defining parameters

Level: \( N \) = \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 12 \)
Sturm bound: \(1620\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(54))\).

Total New Old
Modular forms 759 192 567
Cusp forms 699 192 507
Eisenstein series 60 0 60

Trace form

\( 192 q + 16 q^{2} + 768 q^{4} - 5118 q^{5} + 6816 q^{6} - 1344 q^{7} - 20480 q^{8} - 5088 q^{9} + O(q^{10}) \) \( 192 q + 16 q^{2} + 768 q^{4} - 5118 q^{5} + 6816 q^{6} - 1344 q^{7} - 20480 q^{8} - 5088 q^{9} + 107424 q^{10} + 253278 q^{11} - 56064 q^{12} - 303474 q^{13} + 408512 q^{14} + 970632 q^{15} + 196608 q^{16} - 2601762 q^{17} + 156768 q^{18} + 1193676 q^{19} + 2357760 q^{20} + 5429796 q^{21} - 156672 q^{22} - 14238252 q^{23} + 754545 q^{25} + 14641664 q^{26} + 9101079 q^{27} - 869376 q^{28} - 26787114 q^{29} - 30550464 q^{30} + 21626628 q^{31} + 1048576 q^{32} + 37927413 q^{33} + 5397408 q^{34} - 50349684 q^{35} - 43894272 q^{36} - 16456386 q^{37} + 59995952 q^{38} + 92633592 q^{39} + 27500544 q^{40} + 105796110 q^{41} - 13271424 q^{42} - 129924372 q^{43} - 66152448 q^{44} + 51408486 q^{45} - 1363968 q^{46} + 140007918 q^{47} + 29097984 q^{48} + 362353779 q^{49} + 377552752 q^{50} + 116647182 q^{51} - 77689344 q^{52} - 923082060 q^{53} - 270197568 q^{54} - 41107770 q^{55} + 104579072 q^{56} + 371138697 q^{57} + 389753568 q^{58} - 466061823 q^{59} - 92832768 q^{60} - 667954074 q^{61} - 753978112 q^{62} + 162927984 q^{63} - 855638016 q^{64} + 807870678 q^{65} - 603555840 q^{66} + 352151340 q^{67} + 701886720 q^{68} + 2465037000 q^{69} + 1127141280 q^{70} - 946245336 q^{71} - 212238336 q^{72} - 1295353722 q^{73} - 1768351840 q^{74} - 1479411438 q^{75} + 23329536 q^{76} + 1294427304 q^{77} + 1682989632 q^{78} + 1784868972 q^{79} + 536346624 q^{80} + 1890718524 q^{81} + 726688224 q^{82} + 4452202776 q^{83} - 273024000 q^{84} - 5165280252 q^{85} - 2997491296 q^{86} - 8360794314 q^{87} - 1257394176 q^{88} - 3632197029 q^{89} + 2587065120 q^{90} + 1256602962 q^{91} + 3510070272 q^{92} + 7687750800 q^{93} + 3019963104 q^{94} + 3206429646 q^{95} - 597688320 q^{96} - 10831122570 q^{97} - 4036709520 q^{98} - 943032006 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(54))\)

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
54.10.a \(\chi_{54}(1, \cdot)\) 54.10.a.a 1 1
54.10.a.b 1
54.10.a.c 1
54.10.a.d 1
54.10.a.e 2
54.10.a.f 2
54.10.a.g 2
54.10.a.h 2
54.10.c \(\chi_{54}(19, \cdot)\) 54.10.c.a 8 2
54.10.c.b 10
54.10.e \(\chi_{54}(7, \cdot)\) 54.10.e.a 78 6
54.10.e.b 84

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(54))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(54)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 1}\)