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Properties

Label 57.10
Level 57
Weight 10
Dimension 788
Nonzero newspaces 6
Newform subspaces 14
Sturm bound 2400
Trace bound 1

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Defining parameters

Level: \( N \) = \( 57 = 3 \cdot 19 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 14 \)
Sturm bound: \(2400\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(57))\).

Total New Old
Modular forms 1116 824 292
Cusp forms 1044 788 256
Eisenstein series 72 36 36

Trace form

\( 788 q + 36 q^{2} - 9 q^{3} - 1210 q^{4} + 5688 q^{5} - 8757 q^{6} - 9314 q^{7} + 44784 q^{8} - 26253 q^{9} + O(q^{10}) \) \( 788 q + 36 q^{2} - 9 q^{3} - 1210 q^{4} + 5688 q^{5} - 8757 q^{6} - 9314 q^{7} + 44784 q^{8} - 26253 q^{9} - 39546 q^{10} - 45216 q^{11} - 340209 q^{12} + 1019062 q^{13} - 69984 q^{14} - 860229 q^{15} - 2793010 q^{16} + 1037304 q^{17} + 236196 q^{18} + 2077466 q^{19} - 3749616 q^{20} - 6484221 q^{21} - 10164546 q^{22} + 6770340 q^{23} + 14638311 q^{24} + 14796626 q^{25} - 18917064 q^{26} + 7597314 q^{27} - 43979732 q^{28} + 15828444 q^{29} + 78401412 q^{30} + 2288098 q^{31} - 80502246 q^{32} - 71379747 q^{33} - 68864292 q^{34} + 20780712 q^{35} + 103076721 q^{36} + 63720460 q^{37} + 215042850 q^{38} - 14023980 q^{39} - 247428612 q^{40} - 79682724 q^{41} - 277323507 q^{42} - 61843562 q^{43} + 119200914 q^{44} + 413160201 q^{45} + 516057228 q^{46} + 20078244 q^{47} - 502408314 q^{48} - 443294418 q^{49} - 441476154 q^{50} + 686633634 q^{51} + 249322942 q^{52} - 189177768 q^{53} - 212937237 q^{54} + 68542830 q^{55} + 142289280 q^{56} - 357484185 q^{57} - 647191980 q^{58} + 212773248 q^{59} + 1516901868 q^{60} - 1275989678 q^{61} - 1302389442 q^{62} + 337416363 q^{63} + 3011195390 q^{64} + 2070682524 q^{65} - 830479905 q^{66} - 1137115394 q^{67} - 2340157050 q^{68} - 1363913109 q^{69} - 4056100938 q^{70} - 880584408 q^{71} + 73429389 q^{72} + 2822920120 q^{73} + 2871789768 q^{74} + 2558295252 q^{75} + 4792632386 q^{76} + 4885688556 q^{77} - 1336754835 q^{78} - 5053964210 q^{79} - 7285984560 q^{80} + 1076014611 q^{81} - 7857426168 q^{82} + 2721822588 q^{83} + 2101820499 q^{84} + 2762942670 q^{85} + 4921926282 q^{86} - 672609249 q^{87} - 734983362 q^{88} + 465818148 q^{89} - 2960907552 q^{90} - 11946421474 q^{91} - 5965683822 q^{92} + 4993939989 q^{93} + 26126335116 q^{94} + 4942288620 q^{95} + 20170056294 q^{96} + 256992886 q^{97} - 6494711292 q^{98} - 11270389680 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(57))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
57.10.a \(\chi_{57}(1, \cdot)\) 57.10.a.a 5 1
57.10.a.b 6
57.10.a.c 7
57.10.a.d 8
57.10.d \(\chi_{57}(56, \cdot)\) 57.10.d.a 2 1
57.10.d.b 56
57.10.e \(\chi_{57}(7, \cdot)\) 57.10.e.a 30 2
57.10.e.b 30
57.10.f \(\chi_{57}(8, \cdot)\) 57.10.f.a 2 2
57.10.f.b 2
57.10.f.c 112
57.10.i \(\chi_{57}(4, \cdot)\) 57.10.i.a 84 6
57.10.i.b 96
57.10.j \(\chi_{57}(2, \cdot)\) 57.10.j.a 348 6

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(57))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(57)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 1}\)