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Properties

Label 54.4
Level 54
Weight 4
Dimension 64
Nonzero newspaces 3
Newform subspaces 8
Sturm bound 648
Trace bound 1

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Defining parameters

Level: \( N \) = \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 8 \)
Sturm bound: \(648\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(54))\).

Total New Old
Modular forms 273 64 209
Cusp forms 213 64 149
Eisenstein series 60 0 60

Trace form

\( 64 q - 2 q^{2} + 4 q^{4} - 42 q^{5} + 12 q^{6} + 56 q^{7} + 40 q^{8} + 96 q^{9} + O(q^{10}) \) \( 64 q - 2 q^{2} + 4 q^{4} - 42 q^{5} + 12 q^{6} + 56 q^{7} + 40 q^{8} + 96 q^{9} + 60 q^{10} - 90 q^{11} - 12 q^{12} - 142 q^{13} - 232 q^{14} - 72 q^{15} + 16 q^{16} + 282 q^{17} + 276 q^{18} + 20 q^{19} + 120 q^{20} + 204 q^{21} + 48 q^{22} - 396 q^{23} + 19 q^{25} - 544 q^{26} - 1377 q^{27} + 80 q^{28} - 414 q^{29} - 504 q^{30} + 236 q^{31} - 32 q^{32} + 135 q^{33} - 900 q^{34} - 84 q^{35} + 600 q^{36} - 142 q^{37} + 350 q^{38} + 696 q^{39} + 240 q^{40} + 2226 q^{41} + 912 q^{42} + 1028 q^{43} + 576 q^{44} + 1674 q^{45} + 672 q^{46} + 822 q^{47} + 192 q^{48} + 417 q^{49} - 1406 q^{50} - 3186 q^{51} - 568 q^{52} - 4116 q^{53} - 1008 q^{54} - 306 q^{55} - 928 q^{56} - 3141 q^{57} - 204 q^{58} - 135 q^{59} + 1008 q^{60} + 1082 q^{61} + 3152 q^{62} + 3936 q^{63} - 1088 q^{64} + 8970 q^{65} + 4320 q^{66} + 3908 q^{67} + 876 q^{68} + 6120 q^{69} + 1308 q^{70} + 552 q^{71} - 192 q^{72} - 3166 q^{73} - 3940 q^{74} - 7998 q^{75} - 2260 q^{76} - 11016 q^{77} - 5688 q^{78} - 8476 q^{79} - 384 q^{80} - 6156 q^{81} - 2172 q^{82} - 4560 q^{83} - 2160 q^{84} - 7236 q^{85} - 3532 q^{86} - 2178 q^{87} - 456 q^{88} + 6753 q^{89} + 1260 q^{90} + 4234 q^{91} + 3312 q^{92} + 9696 q^{93} + 6996 q^{94} + 15918 q^{95} + 960 q^{96} + 9506 q^{97} + 2754 q^{98} + 6282 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(54))\)

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
54.4.a \(\chi_{54}(1, \cdot)\) 54.4.a.a 1 1
54.4.a.b 1
54.4.a.c 1
54.4.a.d 1
54.4.c \(\chi_{54}(19, \cdot)\) 54.4.c.a 2 2
54.4.c.b 4
54.4.e \(\chi_{54}(7, \cdot)\) 54.4.e.a 24 6
54.4.e.b 30

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(54))\) into lower level spaces

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