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Properties

Label 5.20
Level 5
Weight 20
Dimension 15
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 40
Trace bound 1

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 20 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(40\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{20}(\Gamma_1(5))\).

Total New Old
Modular forms 21 17 4
Cusp forms 17 15 2
Eisenstein series 4 2 2

Trace form

\( 15 q - 1426 q^{2} - 70372 q^{3} + 1419132 q^{4} - 1806125 q^{5} - 1249520 q^{6} + 159110944 q^{7} - 432759000 q^{8} + 1909300123 q^{9} + O(q^{10}) \) \( 15 q - 1426 q^{2} - 70372 q^{3} + 1419132 q^{4} - 1806125 q^{5} - 1249520 q^{6} + 159110944 q^{7} - 432759000 q^{8} + 1909300123 q^{9} - 1755222250 q^{10} - 360806020 q^{11} + 34268935264 q^{12} - 70818176502 q^{13} + 258118817304 q^{14} - 391801190500 q^{15} + 1234206059440 q^{16} + 936291665534 q^{17} - 5809160185642 q^{18} + 7807366165780 q^{19} - 6387671618500 q^{20} + 1735112132880 q^{21} + 849947048408 q^{22} - 22481077696032 q^{23} + 6534806819040 q^{24} + 44418590484375 q^{25} - 35947227923020 q^{26} - 115566788254600 q^{27} + 167911647644272 q^{28} - 145235335087430 q^{29} + 366330092314000 q^{30} + 38638544656880 q^{31} - 337349702226656 q^{32} + 305281220352976 q^{33} + 10250493897724 q^{34} - 824373287166000 q^{35} + 2026485848744540 q^{36} - 379142637557086 q^{37} - 3622228763368600 q^{38} + 326042816572616 q^{39} - 1378131974815000 q^{40} + 4373386162058230 q^{41} - 8272493269099632 q^{42} + 5024194115931108 q^{43} + 8395890176156944 q^{44} + 12650915888995375 q^{45} - 29683630548979720 q^{46} - 10457356780286296 q^{47} + 36267409908976768 q^{48} + 18161670416823207 q^{49} + 44935285365968750 q^{50} - 79987645515851720 q^{51} - 101380328345593576 q^{52} + 1553621744917778 q^{53} + 243993089437670080 q^{54} + 30460569505811500 q^{55} - 292464868416273600 q^{56} - 43866844325023600 q^{57} - 35466560455978700 q^{58} + 448807013096415740 q^{59} - 27572550156656000 q^{60} - 375202271563766870 q^{61} - 661293594985584672 q^{62} + 252707930425928448 q^{63} + 1396656329791768512 q^{64} + 551367897302313250 q^{65} - 1910458833764964640 q^{66} - 1139262103272878516 q^{67} + 1895976173674409992 q^{68} + 1221896727013268976 q^{69} + 2072970273620883000 q^{70} - 2648414465782000520 q^{71} - 5279093293186620600 q^{72} + 1187325331007472918 q^{73} + 6031229963165079364 q^{74} + 2609484552232437500 q^{75} - 6400448964913817200 q^{76} - 4179052633262859552 q^{77} + 214469126119717456 q^{78} + 7232085167260259120 q^{79} + 1510796026140542000 q^{80} - 4193646574202101385 q^{81} - 8794929960295491812 q^{82} - 2397467032735132212 q^{83} + 21793085150569031904 q^{84} + 2264543612059427750 q^{85} - 10844810777893661920 q^{86} - 5768159345858335000 q^{87} + 5515915220105340000 q^{88} - 1230588610284411690 q^{89} + 4500529955829860750 q^{90} - 3446267777881685920 q^{91} - 1782877520931221616 q^{92} + 16229414747824917216 q^{93} - 10255224591573687416 q^{94} + 4746382914923882500 q^{95} - 20733524406562222720 q^{96} + 3057649965684279854 q^{97} + 17234013451261239982 q^{98} - 39607763857217646484 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{20}^{\mathrm{new}}(\Gamma_1(5))\)

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
5.20.a \(\chi_{5}(1, \cdot)\) 5.20.a.a 3 1
5.20.a.b 4
5.20.b \(\chi_{5}(4, \cdot)\) 5.20.b.a 8 1

Decomposition of \(S_{20}^{\mathrm{old}}(\Gamma_1(5))\) into lower level spaces

\( S_{20}^{\mathrm{old}}(\Gamma_1(5)) \cong \) \(S_{20}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 2}\)