Properties

Label 272.10
Level 272
Weight 10
Dimension 11516
Nonzero newspaces 13
Sturm bound 46080
Trace bound 6

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Defining parameters

Level: \( N \) = \( 272 = 2^{4} \cdot 17 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 13 \)
Sturm bound: \(46080\)
Trace bound: \(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(272))\).

Total New Old
Modular forms 20960 11650 9310
Cusp forms 20512 11516 8996
Eisenstein series 448 134 314

Trace form

\( 11516q - 28q^{2} + 140q^{3} - 368q^{4} + 684q^{5} + 4352q^{6} - 2776q^{7} + 1400q^{8} - 11632q^{9} + O(q^{10}) \) \( 11516q - 28q^{2} + 140q^{3} - 368q^{4} + 684q^{5} + 4352q^{6} - 2776q^{7} + 1400q^{8} - 11632q^{9} - 9400q^{10} - 109756q^{11} - 434344q^{12} + 86124q^{13} + 267048q^{14} - 930912q^{15} + 1634480q^{16} - 172172q^{17} - 4359868q^{18} + 1554428q^{19} + 6555944q^{20} + 594768q^{21} + 68568q^{22} - 2699352q^{23} - 3727744q^{24} + 60928q^{25} + 12695504q^{26} - 2718664q^{27} - 7259088q^{28} - 2181028q^{29} + 9355576q^{30} - 5338872q^{31} + 3311952q^{32} + 7057976q^{33} + 4528172q^{34} + 9687128q^{35} - 47128312q^{36} - 388068q^{37} + 29992672q^{38} - 92859224q^{39} + 23502544q^{40} - 9595736q^{41} - 210798352q^{42} + 227358516q^{43} + 188446680q^{44} + 5960804q^{45} - 30864824q^{46} - 473932472q^{47} - 15663088q^{48} + 246796580q^{49} + 12579028q^{50} + 230029060q^{51} + 56568792q^{52} - 103421652q^{53} - 210622048q^{54} + 5677816q^{55} - 53022544q^{56} - 929439944q^{57} + 356543536q^{58} + 112546980q^{59} - 458068256q^{60} + 1081912268q^{61} + 273577856q^{62} + 1269342096q^{63} + 698585824q^{64} - 498484656q^{65} - 384547720q^{66} - 1268065676q^{67} + 285757456q^{68} - 2369429560q^{69} - 1212102432q^{70} + 772755192q^{71} - 1764151400q^{72} + 1965149544q^{73} - 247821752q^{74} + 3484636716q^{75} + 906538168q^{76} - 2186170096q^{77} + 3470049576q^{78} - 5492048840q^{79} + 1400545680q^{80} + 2501748956q^{81} + 1348575136q^{82} + 6400747996q^{83} - 2563839856q^{84} - 4253471532q^{85} - 487961416q^{86} + 2834566824q^{87} - 3562294288q^{88} - 1146752216q^{89} - 6168174416q^{90} - 7481989792q^{91} + 6263268976q^{92} - 135496520q^{93} + 4136920512q^{94} + 14482767552q^{95} + 7792966272q^{96} + 1456363696q^{97} + 6201264172q^{98} - 13045146524q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(272))\)

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
272.10.a \(\chi_{272}(1, \cdot)\) 272.10.a.a 2 1
272.10.a.b 3
272.10.a.c 3
272.10.a.d 4
272.10.a.e 5
272.10.a.f 5
272.10.a.g 7
272.10.a.h 7
272.10.a.i 8
272.10.a.j 9
272.10.a.k 9
272.10.a.l 10
272.10.b \(\chi_{272}(33, \cdot)\) 272.10.b.a 6 1
272.10.b.b 8
272.10.b.c 12
272.10.b.d 14
272.10.b.e 20
272.10.b.f 20
272.10.c \(\chi_{272}(137, \cdot)\) None 0 1
272.10.h \(\chi_{272}(169, \cdot)\) None 0 1
272.10.j \(\chi_{272}(13, \cdot)\) n/a 644 2
272.10.l \(\chi_{272}(69, \cdot)\) n/a 576 2
272.10.m \(\chi_{272}(89, \cdot)\) None 0 2
272.10.o \(\chi_{272}(81, \cdot)\) n/a 160 2
272.10.r \(\chi_{272}(101, \cdot)\) n/a 644 2
272.10.s \(\chi_{272}(149, \cdot)\) n/a 644 2
272.10.v \(\chi_{272}(49, \cdot)\) n/a 320 4
272.10.w \(\chi_{272}(189, \cdot)\) n/a 1288 4
272.10.y \(\chi_{272}(53, \cdot)\) n/a 1288 4
272.10.ba \(\chi_{272}(9, \cdot)\) None 0 4
272.10.bd \(\chi_{272}(3, \cdot)\) n/a 2576 8
272.10.bf \(\chi_{272}(31, \cdot)\) n/a 648 8
272.10.bg \(\chi_{272}(7, \cdot)\) None 0 8
272.10.bj \(\chi_{272}(107, \cdot)\) n/a 2576 8

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

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(272))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_1(272)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 2}\)