Properties

Label 55.17
Level 55
Weight 17
Dimension 1702
Nonzero newspaces 6
Sturm bound 4080
Trace bound 1

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Defining parameters

Level: \( N \) = \( 55 = 5 \cdot 11 \)
Weight: \( k \) = \( 17 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(4080\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(\Gamma_1(55))\).

Total New Old
Modular forms 1960 1754 206
Cusp forms 1880 1702 178
Eisenstein series 80 52 28

Trace form

\( 1702 q - 6 q^{2} - 15826 q^{3} - 10 q^{4} - 385775 q^{5} - 3960526 q^{6} - 4997756 q^{7} - 39961810 q^{8} + 129842250 q^{9} + O(q^{10}) \) \( 1702 q - 6 q^{2} - 15826 q^{3} - 10 q^{4} - 385775 q^{5} - 3960526 q^{6} - 4997756 q^{7} - 39961810 q^{8} + 129842250 q^{9} - 797455680 q^{10} + 107910592 q^{11} + 1237277724 q^{12} - 4760636 q^{13} + 1711974680 q^{14} + 11859249455 q^{15} - 35451824918 q^{16} + 26979336204 q^{17} - 102460407356 q^{18} - 63999132970 q^{19} + 180856539400 q^{20} - 267304572136 q^{21} - 454495363406 q^{22} - 120353741146 q^{23} + 1845301042890 q^{24} - 291865178765 q^{25} - 3867155613316 q^{26} + 1434369362420 q^{27} + 6623036029876 q^{28} - 4892022755440 q^{29} - 4929759147600 q^{30} + 11139680998294 q^{31} + 4049071279964 q^{32} - 19548500735756 q^{33} + 14595669624740 q^{34} - 12404543155790 q^{35} - 22726172157628 q^{36} + 36528095919174 q^{37} - 15969838049740 q^{38} - 60471365306340 q^{39} - 47413943900760 q^{40} - 29181197605036 q^{41} + 196980444562368 q^{42} + 153526871565484 q^{43} - 150319374614260 q^{44} - 268140824133960 q^{45} + 89693468667804 q^{46} + 59657745039924 q^{47} + 707995977579244 q^{48} - 118690561199540 q^{49} - 781495579594370 q^{50} - 284242659862726 q^{51} + 239262533094664 q^{52} + 652095381400764 q^{53} - 160953023001875 q^{55} - 1175300205057240 q^{56} + 1745337537739630 q^{57} + 2544286215272100 q^{58} - 305174491534300 q^{59} - 4420948545814200 q^{60} - 355538789553696 q^{61} + 2027372094908428 q^{62} + 5148419025285724 q^{63} + 1816201464816510 q^{64} - 2741184066144700 q^{65} - 7027907507183716 q^{66} - 1108841413400506 q^{67} + 1897780932378356 q^{68} + 3488030297386490 q^{69} + 8149105889863960 q^{70} + 6889465335221594 q^{71} - 27700744964497990 q^{72} - 1579293542418556 q^{73} + 1344919935418880 q^{74} + 5145505913306625 q^{75} + 467501593800440 q^{76} + 426683540009304 q^{77} - 26701184940701112 q^{78} + 5235347022606500 q^{79} + 37268768953705880 q^{80} + 27909718347136162 q^{81} - 45134389694885862 q^{82} - 24134580809361906 q^{83} + 19860088759552920 q^{84} + 42727521763650750 q^{85} + 24012336406357474 q^{86} - 34655066536423700 q^{87} - 20574596015100490 q^{88} + 3177885941001610 q^{89} + 48938998548507780 q^{90} + 9329036824647724 q^{91} - 45072807073244936 q^{92} + 44246438460591298 q^{93} - 57854505912816960 q^{94} + 23227970049199590 q^{95} + 207954975474519064 q^{96} + 22568013408604044 q^{97} - 96407117869751724 q^{98} - 50496800724069850 q^{99} + O(q^{100}) \)

Decomposition of \(S_{17}^{\mathrm{new}}(\Gamma_1(55))\)

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 available newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
55.17.c \(\chi_{55}(21, \cdot)\) 55.17.c.a 64 1
55.17.d \(\chi_{55}(54, \cdot)\) 55.17.d.a 1 1
55.17.d.b 1
55.17.d.c 2
55.17.d.d 2
55.17.d.e 88
55.17.f \(\chi_{55}(12, \cdot)\) n/a 160 2
55.17.h \(\chi_{55}(19, \cdot)\) n/a 376 4
55.17.i \(\chi_{55}(6, \cdot)\) n/a 256 4
55.17.k \(\chi_{55}(3, \cdot)\) n/a 752 8

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{17}^{\mathrm{old}}(\Gamma_1(55))\) into lower level spaces

\( S_{17}^{\mathrm{old}}(\Gamma_1(55)) \cong \) \(S_{17}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{17}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)