Properties

Label 57.2
Level 57
Weight 2
Dimension 71
Nonzero newspaces 6
Newforms 11
Sturm bound 480
Trace bound 3

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Defining parameters

Level: \( N \) = \( 57 = 3 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 6 \)
Newforms: \( 11 \)
Sturm bound: \(480\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(57))\).

Total New Old
Modular forms 156 107 49
Cusp forms 85 71 14
Eisenstein series 71 36 35

Trace form

\(71q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut -\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 26q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut -\mathstrut 10q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(71q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 10q^{3} \) \(\mathstrut -\mathstrut 25q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut -\mathstrut 26q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut -\mathstrut 10q^{9} \) \(\mathstrut -\mathstrut 36q^{10} \) \(\mathstrut -\mathstrut 12q^{11} \) \(\mathstrut -\mathstrut 4q^{12} \) \(\mathstrut -\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 23q^{16} \) \(\mathstrut -\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 30q^{20} \) \(\mathstrut +\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 6q^{23} \) \(\mathstrut +\mathstrut 12q^{24} \) \(\mathstrut -\mathstrut 13q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut +\mathstrut 2q^{27} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 6q^{29} \) \(\mathstrut +\mathstrut 36q^{30} \) \(\mathstrut -\mathstrut 14q^{31} \) \(\mathstrut +\mathstrut 27q^{32} \) \(\mathstrut +\mathstrut 33q^{33} \) \(\mathstrut +\mathstrut 18q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 56q^{36} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 69q^{38} \) \(\mathstrut +\mathstrut 22q^{39} \) \(\mathstrut +\mathstrut 54q^{40} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut +\mathstrut 57q^{42} \) \(\mathstrut +\mathstrut 10q^{43} \) \(\mathstrut +\mathstrut 6q^{44} \) \(\mathstrut +\mathstrut 12q^{45} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut -\mathstrut 40q^{48} \) \(\mathstrut -\mathstrut 39q^{49} \) \(\mathstrut -\mathstrut 39q^{50} \) \(\mathstrut -\mathstrut 63q^{51} \) \(\mathstrut -\mathstrut 116q^{52} \) \(\mathstrut -\mathstrut 54q^{53} \) \(\mathstrut -\mathstrut 66q^{54} \) \(\mathstrut -\mathstrut 90q^{55} \) \(\mathstrut -\mathstrut 120q^{56} \) \(\mathstrut -\mathstrut 73q^{57} \) \(\mathstrut -\mathstrut 126q^{58} \) \(\mathstrut -\mathstrut 60q^{59} \) \(\mathstrut -\mathstrut 114q^{60} \) \(\mathstrut -\mathstrut 20q^{61} \) \(\mathstrut -\mathstrut 6q^{62} \) \(\mathstrut -\mathstrut 41q^{63} \) \(\mathstrut -\mathstrut q^{64} \) \(\mathstrut +\mathstrut 24q^{65} \) \(\mathstrut -\mathstrut 45q^{66} \) \(\mathstrut +\mathstrut 58q^{67} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 54q^{70} \) \(\mathstrut +\mathstrut 39q^{72} \) \(\mathstrut +\mathstrut 70q^{73} \) \(\mathstrut +\mathstrut 30q^{74} \) \(\mathstrut +\mathstrut 53q^{75} \) \(\mathstrut +\mathstrut 29q^{76} \) \(\mathstrut +\mathstrut 102q^{77} \) \(\mathstrut +\mathstrut 93q^{78} \) \(\mathstrut +\mathstrut 106q^{79} \) \(\mathstrut +\mathstrut 66q^{80} \) \(\mathstrut +\mathstrut 26q^{81} \) \(\mathstrut +\mathstrut 198q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 151q^{84} \) \(\mathstrut +\mathstrut 90q^{85} \) \(\mathstrut +\mathstrut 66q^{86} \) \(\mathstrut +\mathstrut 105q^{87} \) \(\mathstrut +\mathstrut 126q^{88} \) \(\mathstrut +\mathstrut 72q^{89} \) \(\mathstrut +\mathstrut 36q^{90} \) \(\mathstrut +\mathstrut 38q^{91} \) \(\mathstrut +\mathstrut 66q^{92} \) \(\mathstrut +\mathstrut 61q^{93} \) \(\mathstrut +\mathstrut 36q^{94} \) \(\mathstrut -\mathstrut 60q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut -\mathstrut 62q^{97} \) \(\mathstrut -\mathstrut 27q^{98} \) \(\mathstrut -\mathstrut 12q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)

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
57.2.a \(\chi_{57}(1, \cdot)\) 57.2.a.a 1 1
57.2.a.b 1
57.2.a.c 1
57.2.d \(\chi_{57}(56, \cdot)\) 57.2.d.a 4 1
57.2.e \(\chi_{57}(7, \cdot)\) 57.2.e.a 2 2
57.2.e.b 6
57.2.f \(\chi_{57}(8, \cdot)\) 57.2.f.a 8 2
57.2.i \(\chi_{57}(4, \cdot)\) 57.2.i.a 6 6
57.2.i.b 12
57.2.j \(\chi_{57}(2, \cdot)\) 57.2.j.a 6 6
57.2.j.b 24

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(57))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(57)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)