↑

Properties

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

Downloads

Learn more

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

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

Display 100 coefficients 10 coefficients

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 available 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

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