Properties

Label 54.2
Level 54
Weight 2
Dimension 22
Nonzero newspaces 3
Newforms 5
Sturm bound 324
Trace bound 2

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Defining parameters

Level: \( N \) = \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 3 \)
Newforms: \( 5 \)
Sturm bound: \(324\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(54))\).

Total New Old
Modular forms 111 22 89
Cusp forms 52 22 30
Eisenstein series 59 0 59

Trace form

\(22q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 5q^{8} \) \(\mathstrut -\mathstrut 12q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(22q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut +\mathstrut q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut -\mathstrut 5q^{8} \) \(\mathstrut -\mathstrut 12q^{9} \) \(\mathstrut -\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut -\mathstrut 3q^{12} \) \(\mathstrut -\mathstrut 10q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut -\mathstrut 18q^{15} \) \(\mathstrut +\mathstrut q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut +\mathstrut 6q^{18} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut +\mathstrut 12q^{20} \) \(\mathstrut +\mathstrut 24q^{21} \) \(\mathstrut +\mathstrut 18q^{23} \) \(\mathstrut -\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 32q^{26} \) \(\mathstrut +\mathstrut 27q^{27} \) \(\mathstrut +\mathstrut 2q^{28} \) \(\mathstrut +\mathstrut 36q^{29} \) \(\mathstrut +\mathstrut 36q^{30} \) \(\mathstrut -\mathstrut 4q^{31} \) \(\mathstrut +\mathstrut q^{32} \) \(\mathstrut +\mathstrut 27q^{33} \) \(\mathstrut -\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 6q^{36} \) \(\mathstrut -\mathstrut 4q^{37} \) \(\mathstrut -\mathstrut 13q^{38} \) \(\mathstrut -\mathstrut 42q^{39} \) \(\mathstrut -\mathstrut 6q^{40} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut -\mathstrut 24q^{42} \) \(\mathstrut -\mathstrut 28q^{43} \) \(\mathstrut -\mathstrut 6q^{47} \) \(\mathstrut -\mathstrut 6q^{48} \) \(\mathstrut -\mathstrut 27q^{49} \) \(\mathstrut -\mathstrut 41q^{50} \) \(\mathstrut -\mathstrut 10q^{52} \) \(\mathstrut -\mathstrut 48q^{53} \) \(\mathstrut -\mathstrut 36q^{54} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 4q^{56} \) \(\mathstrut -\mathstrut 9q^{57} \) \(\mathstrut -\mathstrut 18q^{58} \) \(\mathstrut +\mathstrut 9q^{59} \) \(\mathstrut -\mathstrut 18q^{60} \) \(\mathstrut -\mathstrut 10q^{61} \) \(\mathstrut -\mathstrut 16q^{62} \) \(\mathstrut -\mathstrut 6q^{63} \) \(\mathstrut -\mathstrut 5q^{64} \) \(\mathstrut +\mathstrut 6q^{65} \) \(\mathstrut +\mathstrut 50q^{67} \) \(\mathstrut -\mathstrut 15q^{68} \) \(\mathstrut +\mathstrut 18q^{69} \) \(\mathstrut +\mathstrut 42q^{70} \) \(\mathstrut +\mathstrut 48q^{71} \) \(\mathstrut +\mathstrut 24q^{72} \) \(\mathstrut -\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 26q^{74} \) \(\mathstrut +\mathstrut 12q^{75} \) \(\mathstrut +\mathstrut 23q^{76} \) \(\mathstrut +\mathstrut 36q^{77} \) \(\mathstrut +\mathstrut 36q^{78} \) \(\mathstrut +\mathstrut 92q^{79} \) \(\mathstrut +\mathstrut 12q^{80} \) \(\mathstrut +\mathstrut 30q^{82} \) \(\mathstrut +\mathstrut 12q^{83} \) \(\mathstrut +\mathstrut 72q^{85} \) \(\mathstrut +\mathstrut 26q^{86} \) \(\mathstrut +\mathstrut 36q^{87} \) \(\mathstrut +\mathstrut 27q^{88} \) \(\mathstrut -\mathstrut 15q^{89} \) \(\mathstrut +\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 2q^{91} \) \(\mathstrut -\mathstrut 6q^{93} \) \(\mathstrut +\mathstrut 30q^{94} \) \(\mathstrut +\mathstrut 6q^{95} \) \(\mathstrut +\mathstrut 6q^{96} \) \(\mathstrut +\mathstrut 20q^{97} \) \(\mathstrut -\mathstrut 9q^{98} \) \(\mathstrut -\mathstrut 36q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
54.2.a \(\chi_{54}(1, \cdot)\) 54.2.a.a 1 1
54.2.a.b 1
54.2.c \(\chi_{54}(19, \cdot)\) 54.2.c.a 2 2
54.2.e \(\chi_{54}(7, \cdot)\) 54.2.e.a 6 6
54.2.e.b 12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(54))\) into lower level spaces

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