Properties

Label 54.3
Level 54
Weight 3
Dimension 42
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 486
Trace bound 1

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Defining parameters

Level: \( N \) = \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(486\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(54))\).

Total New Old
Modular forms 192 42 150
Cusp forms 132 42 90
Eisenstein series 60 0 60

Trace form

\( 42 q + 36 q^{5} + 12 q^{6} + 12 q^{7} - 12 q^{9} + O(q^{10}) \) \( 42 q + 36 q^{5} + 12 q^{6} + 12 q^{7} - 12 q^{9} - 24 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 72 q^{14} - 18 q^{15} - 48 q^{18} + 18 q^{19} - 36 q^{20} - 228 q^{21} + 48 q^{22} - 198 q^{23} - 72 q^{25} + 54 q^{27} - 12 q^{28} + 126 q^{29} + 144 q^{30} - 72 q^{31} + 324 q^{33} + 24 q^{34} + 486 q^{35} + 168 q^{36} + 78 q^{37} + 252 q^{38} + 102 q^{39} + 48 q^{40} + 36 q^{41} + 48 q^{42} + 72 q^{43} - 378 q^{45} - 48 q^{46} - 432 q^{47} - 24 q^{48} + 12 q^{49} - 54 q^{51} + 24 q^{52} - 36 q^{54} + 36 q^{55} - 144 q^{56} + 72 q^{57} - 24 q^{58} + 126 q^{59} + 36 q^{60} - 36 q^{61} + 318 q^{63} + 96 q^{64} - 72 q^{65} - 432 q^{66} - 738 q^{67} - 252 q^{68} - 522 q^{69} - 588 q^{70} - 648 q^{71} - 192 q^{72} - 276 q^{73} - 576 q^{74} - 438 q^{75} - 228 q^{76} - 252 q^{77} - 288 q^{78} + 96 q^{79} + 324 q^{81} + 192 q^{82} + 972 q^{83} + 216 q^{84} + 900 q^{85} + 648 q^{86} + 1062 q^{87} + 120 q^{88} + 648 q^{89} + 720 q^{90} + 204 q^{91} + 360 q^{92} + 462 q^{93} + 612 q^{94} + 72 q^{95} + 96 q^{96} + 618 q^{97} + 648 q^{98} + 126 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(54))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
54.3.b \(\chi_{54}(53, \cdot)\) 54.3.b.a 2 1
54.3.d \(\chi_{54}(17, \cdot)\) 54.3.d.a 4 2
54.3.f \(\chi_{54}(5, \cdot)\) 54.3.f.a 36 6

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(54))\) into lower level spaces

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