Properties

Label 57.3
Level 57
Weight 3
Dimension 162
Nonzero newspaces 6
Newform subspaces 11
Sturm bound 720
Trace bound 3

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Defining parameters

Level: \( N \) = \( 57 = 3 \cdot 19 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 11 \)
Sturm bound: \(720\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(57))\).

Total New Old
Modular forms 276 194 82
Cusp forms 204 162 42
Eisenstein series 72 32 40

Trace form

\( 162 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 18 q^{7} - 9 q^{9} + O(q^{10}) \) \( 162 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 18 q^{7} - 9 q^{9} - 18 q^{10} - 81 q^{12} - 138 q^{13} - 144 q^{14} - 63 q^{15} - 162 q^{16} - 18 q^{17} - 18 q^{18} + 24 q^{19} + 144 q^{20} + 54 q^{21} + 198 q^{22} + 90 q^{23} + 207 q^{24} + 234 q^{25} + 288 q^{26} - 72 q^{27} - 264 q^{28} - 288 q^{29} - 450 q^{30} - 234 q^{31} - 450 q^{32} - 225 q^{33} - 288 q^{34} - 144 q^{35} - 63 q^{36} - 36 q^{37} + 126 q^{38} + 90 q^{39} + 432 q^{40} + 144 q^{41} + 441 q^{42} + 414 q^{43} + 630 q^{44} + 720 q^{45} + 792 q^{46} + 360 q^{47} + 1188 q^{48} + 414 q^{49} + 702 q^{50} + 342 q^{51} - 18 q^{52} + 99 q^{54} - 18 q^{55} - 54 q^{57} - 36 q^{58} - 630 q^{60} - 858 q^{61} - 1170 q^{62} - 405 q^{63} - 1602 q^{64} - 1080 q^{65} - 1377 q^{66} - 1170 q^{67} - 882 q^{68} - 792 q^{69} - 1098 q^{70} - 288 q^{71} - 747 q^{72} - 342 q^{73} - 144 q^{74} - 18 q^{75} + 162 q^{76} + 54 q^{77} - 279 q^{78} + 114 q^{79} - 792 q^{80} - 477 q^{81} + 1008 q^{82} - 18 q^{83} - 117 q^{84} + 774 q^{85} + 810 q^{86} + 351 q^{87} + 774 q^{88} + 1242 q^{89} + 126 q^{90} + 1302 q^{91} + 1242 q^{92} + 459 q^{93} + 648 q^{94} + 54 q^{95} + 1494 q^{96} + 144 q^{97} + 576 q^{98} + 1233 q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(57))\)

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
57.3.b \(\chi_{57}(20, \cdot)\) 57.3.b.a 12 1
57.3.c \(\chi_{57}(37, \cdot)\) 57.3.c.a 2 1
57.3.c.b 4
57.3.g \(\chi_{57}(31, \cdot)\) 57.3.g.a 6 2
57.3.g.b 6
57.3.h \(\chi_{57}(11, \cdot)\) 57.3.h.a 8 2
57.3.h.b 16
57.3.k \(\chi_{57}(10, \cdot)\) 57.3.k.a 18 6
57.3.k.b 24
57.3.l \(\chi_{57}(5, \cdot)\) 57.3.l.a 6 6
57.3.l.b 60

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(57))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(57)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)