Properties

Label 55.6
Level 55
Weight 6
Dimension 514
Nonzero newspaces 6
Newform subspaces 12
Sturm bound 1440
Trace bound 1

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Defining parameters

Level: \( N \) = \( 55 = 5 \cdot 11 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 12 \)
Sturm bound: \(1440\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(55))\).

Total New Old
Modular forms 640 570 70
Cusp forms 560 514 46
Eisenstein series 80 56 24

Trace form

\( 514 q - 14 q^{2} - 2 q^{3} + 94 q^{4} + 115 q^{5} - 502 q^{6} - 984 q^{7} - 90 q^{8} + 2156 q^{9} + O(q^{10}) \) \( 514 q - 14 q^{2} - 2 q^{3} + 94 q^{4} + 115 q^{5} - 502 q^{6} - 984 q^{7} - 90 q^{8} + 2156 q^{9} + 1770 q^{10} + 504 q^{11} + 396 q^{12} - 1592 q^{13} - 1372 q^{14} - 6195 q^{15} - 12566 q^{16} - 164 q^{17} + 6488 q^{18} + 3220 q^{19} + 7910 q^{20} + 23908 q^{21} + 25426 q^{22} + 14418 q^{23} - 8750 q^{24} - 17835 q^{25} - 70232 q^{26} - 50630 q^{27} - 54048 q^{28} + 26080 q^{29} + 45460 q^{30} + 28458 q^{31} + 142356 q^{32} + 84618 q^{33} - 2852 q^{34} - 36490 q^{35} - 157576 q^{36} - 69234 q^{37} - 125140 q^{38} - 50148 q^{39} - 30260 q^{40} + 40228 q^{41} + 63112 q^{42} + 76448 q^{43} + 288724 q^{44} + 203390 q^{45} + 224628 q^{46} + 101496 q^{47} + 68388 q^{48} - 156346 q^{49} - 188790 q^{50} - 148052 q^{51} - 124184 q^{52} - 224912 q^{53} - 615540 q^{54} - 214775 q^{55} - 442960 q^{56} - 106620 q^{57} - 125740 q^{58} + 36590 q^{59} + 251400 q^{60} + 245628 q^{61} + 622072 q^{62} + 604528 q^{63} + 837934 q^{64} + 280720 q^{65} + 174208 q^{66} + 97066 q^{67} - 103088 q^{68} - 356418 q^{69} - 388600 q^{70} + 79998 q^{71} + 16430 q^{72} + 46328 q^{73} - 452272 q^{74} + 148315 q^{75} - 520980 q^{76} - 758804 q^{77} - 829504 q^{78} - 570200 q^{79} + 2560 q^{80} + 997314 q^{81} + 1168602 q^{82} + 551888 q^{83} - 268652 q^{84} + 45520 q^{85} - 570342 q^{86} - 56100 q^{87} - 258570 q^{88} - 280730 q^{89} - 1047810 q^{90} - 314432 q^{91} - 146404 q^{92} + 263986 q^{93} + 645068 q^{94} + 600520 q^{95} + 2763768 q^{96} + 527366 q^{97} + 784132 q^{98} + 570706 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(55))\)

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
55.6.a \(\chi_{55}(1, \cdot)\) 55.6.a.a 3 1
55.6.a.b 4
55.6.a.c 5
55.6.a.d 6
55.6.b \(\chi_{55}(34, \cdot)\) 55.6.b.a 10 1
55.6.b.b 14
55.6.e \(\chi_{55}(32, \cdot)\) 55.6.e.a 4 2
55.6.e.b 52
55.6.g \(\chi_{55}(16, \cdot)\) 55.6.g.a 40 4
55.6.g.b 40
55.6.j \(\chi_{55}(4, \cdot)\) 55.6.j.a 112 4
55.6.l \(\chi_{55}(2, \cdot)\) 55.6.l.a 224 8

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(55))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(55)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)