Properties

Label 55.2
Level 55
Weight 2
Dimension 79
Nonzero newspaces 6
Newforms 9
Sturm bound 480
Trace bound 2

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Defining parameters

Level: \( N \) = \( 55 = 5 \cdot 11 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newforms: \( 9 \)
Sturm bound: \(480\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(55))\).

Total New Old
Modular forms 160 135 25
Cusp forms 81 79 2
Eisenstein series 79 56 23

Trace form

\(79q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 14q^{3} \) \(\mathstrut -\mathstrut 17q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 32q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 5q^{8} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(79q \) \(\mathstrut -\mathstrut 13q^{2} \) \(\mathstrut -\mathstrut 14q^{3} \) \(\mathstrut -\mathstrut 17q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut -\mathstrut 32q^{6} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 5q^{8} \) \(\mathstrut -\mathstrut 3q^{9} \) \(\mathstrut -\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 31q^{11} \) \(\mathstrut -\mathstrut 8q^{12} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut q^{15} \) \(\mathstrut -\mathstrut q^{16} \) \(\mathstrut +\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 13q^{20} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut -\mathstrut 14q^{23} \) \(\mathstrut +\mathstrut 40q^{24} \) \(\mathstrut +\mathstrut 14q^{25} \) \(\mathstrut +\mathstrut 18q^{26} \) \(\mathstrut +\mathstrut 10q^{27} \) \(\mathstrut +\mathstrut 44q^{28} \) \(\mathstrut +\mathstrut 10q^{29} \) \(\mathstrut +\mathstrut 38q^{30} \) \(\mathstrut -\mathstrut 22q^{31} \) \(\mathstrut +\mathstrut 27q^{32} \) \(\mathstrut +\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 6q^{34} \) \(\mathstrut +\mathstrut 22q^{35} \) \(\mathstrut +\mathstrut 59q^{36} \) \(\mathstrut +\mathstrut 12q^{37} \) \(\mathstrut +\mathstrut 40q^{38} \) \(\mathstrut +\mathstrut 44q^{39} \) \(\mathstrut -\mathstrut 25q^{40} \) \(\mathstrut +\mathstrut 18q^{41} \) \(\mathstrut +\mathstrut 44q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 27q^{44} \) \(\mathstrut -\mathstrut 33q^{45} \) \(\mathstrut -\mathstrut 52q^{46} \) \(\mathstrut -\mathstrut 48q^{47} \) \(\mathstrut -\mathstrut 64q^{48} \) \(\mathstrut -\mathstrut 57q^{49} \) \(\mathstrut -\mathstrut 43q^{50} \) \(\mathstrut -\mathstrut 52q^{51} \) \(\mathstrut -\mathstrut 98q^{52} \) \(\mathstrut -\mathstrut 14q^{53} \) \(\mathstrut -\mathstrut 60q^{54} \) \(\mathstrut -\mathstrut 46q^{55} \) \(\mathstrut -\mathstrut 120q^{56} \) \(\mathstrut -\mathstrut 20q^{57} \) \(\mathstrut -\mathstrut 90q^{58} \) \(\mathstrut -\mathstrut 30q^{59} \) \(\mathstrut -\mathstrut 38q^{60} \) \(\mathstrut -\mathstrut 82q^{61} \) \(\mathstrut +\mathstrut 24q^{62} \) \(\mathstrut -\mathstrut 24q^{63} \) \(\mathstrut -\mathstrut 37q^{64} \) \(\mathstrut -\mathstrut 14q^{65} \) \(\mathstrut +\mathstrut 8q^{66} \) \(\mathstrut -\mathstrut 18q^{67} \) \(\mathstrut +\mathstrut 34q^{68} \) \(\mathstrut +\mathstrut 34q^{69} \) \(\mathstrut +\mathstrut 56q^{70} \) \(\mathstrut +\mathstrut 38q^{71} \) \(\mathstrut +\mathstrut 55q^{72} \) \(\mathstrut +\mathstrut 46q^{73} \) \(\mathstrut +\mathstrut 106q^{74} \) \(\mathstrut +\mathstrut 71q^{75} \) \(\mathstrut +\mathstrut 100q^{76} \) \(\mathstrut +\mathstrut 72q^{77} \) \(\mathstrut +\mathstrut 112q^{78} \) \(\mathstrut +\mathstrut 80q^{79} \) \(\mathstrut +\mathstrut 139q^{80} \) \(\mathstrut +\mathstrut 79q^{81} \) \(\mathstrut +\mathstrut 74q^{82} \) \(\mathstrut +\mathstrut 76q^{83} \) \(\mathstrut +\mathstrut 116q^{84} \) \(\mathstrut +\mathstrut 72q^{85} \) \(\mathstrut +\mathstrut 68q^{86} \) \(\mathstrut +\mathstrut 100q^{87} \) \(\mathstrut +\mathstrut 145q^{88} \) \(\mathstrut +\mathstrut 20q^{89} \) \(\mathstrut -\mathstrut 9q^{90} \) \(\mathstrut +\mathstrut 48q^{91} \) \(\mathstrut +\mathstrut 52q^{92} \) \(\mathstrut +\mathstrut 2q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 52q^{96} \) \(\mathstrut -\mathstrut 28q^{97} \) \(\mathstrut -\mathstrut 81q^{98} \) \(\mathstrut -\mathstrut 73q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)

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
55.2.a \(\chi_{55}(1, \cdot)\) 55.2.a.a 1 1
55.2.a.b 2
55.2.b \(\chi_{55}(34, \cdot)\) 55.2.b.a 4 1
55.2.e \(\chi_{55}(32, \cdot)\) 55.2.e.a 4 2
55.2.e.b 4
55.2.g \(\chi_{55}(16, \cdot)\) 55.2.g.a 8 4
55.2.g.b 8
55.2.j \(\chi_{55}(4, \cdot)\) 55.2.j.a 16 4
55.2.l \(\chi_{55}(2, \cdot)\) 55.2.l.a 32 8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(55))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(55)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)