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Properties

Label 169.6
Level 169
Weight 6
Dimension 5743
Nonzero newspaces 8
Sturm bound 14196
Trace bound 1

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Defining parameters

Level: \( N \) = \( 169 = 13^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(14196\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(169))\).

Total New Old
Modular forms 6029 5948 81
Cusp forms 5801 5743 58
Eisenstein series 228 205 23

Trace form

\( 5743 q - 66 q^{2} - 66 q^{3} - 66 q^{4} - 66 q^{5} - 66 q^{6} + 530 q^{7} - 1218 q^{8} - 1362 q^{9} + O(q^{10}) \) \( 5743 q - 66 q^{2} - 66 q^{3} - 66 q^{4} - 66 q^{5} - 66 q^{6} + 530 q^{7} - 1218 q^{8} - 1362 q^{9} - 186 q^{10} + 1002 q^{11} + 5706 q^{12} + 1500 q^{13} + 930 q^{14} - 2442 q^{15} - 10306 q^{16} + 2328 q^{17} - 6942 q^{18} - 10042 q^{19} - 11058 q^{20} - 7398 q^{21} - 1806 q^{22} + 6390 q^{23} + 48798 q^{24} + 18696 q^{25} + 17898 q^{26} + 30186 q^{27} + 45002 q^{28} - 396 q^{29} - 106338 q^{30} - 59710 q^{31} - 158598 q^{32} - 82710 q^{33} - 36786 q^{34} + 38994 q^{35} + 190614 q^{36} + 71912 q^{37} + 103914 q^{38} + 76920 q^{39} + 191538 q^{40} + 5376 q^{41} - 132294 q^{42} - 168998 q^{43} - 273846 q^{44} - 269916 q^{45} - 210906 q^{46} - 85470 q^{47} - 34146 q^{48} + 140026 q^{49} + 401850 q^{50} + 504282 q^{51} + 242422 q^{52} + 114546 q^{53} - 69918 q^{54} - 74574 q^{55} - 288630 q^{56} - 305574 q^{57} - 351738 q^{58} - 191598 q^{59} - 352302 q^{60} - 360456 q^{61} + 437310 q^{62} + 413202 q^{63} + 398682 q^{64} + 77229 q^{65} + 248922 q^{66} + 160238 q^{67} - 687510 q^{68} - 298494 q^{69} - 491190 q^{70} - 199722 q^{71} - 497286 q^{72} + 91382 q^{73} + 575070 q^{74} + 311730 q^{75} + 179414 q^{76} + 241602 q^{77} + 452814 q^{78} - 34470 q^{79} + 696738 q^{80} + 419382 q^{81} - 136914 q^{82} - 198342 q^{83} - 271398 q^{84} + 158688 q^{85} - 128670 q^{86} + 15438 q^{87} - 473046 q^{88} - 769218 q^{89} - 1826382 q^{90} - 449462 q^{91} - 394302 q^{92} - 810030 q^{93} + 616662 q^{94} + 546582 q^{95} + 1155450 q^{96} + 394958 q^{97} + 1194534 q^{98} + 734058 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(169))\)

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
169.6.a \(\chi_{169}(1, \cdot)\) 169.6.a.a 2 1
169.6.a.b 3
169.6.a.c 4
169.6.a.d 4
169.6.a.e 6
169.6.a.f 10
169.6.a.g 15
169.6.a.h 15
169.6.b \(\chi_{169}(168, \cdot)\) 169.6.b.a 4 1
169.6.b.b 6
169.6.b.c 8
169.6.b.d 10
169.6.b.e 30
169.6.c \(\chi_{169}(22, \cdot)\) n/a 120 2
169.6.e \(\chi_{169}(23, \cdot)\) n/a 118 2
169.6.g \(\chi_{169}(14, \cdot)\) n/a 900 12
169.6.h \(\chi_{169}(12, \cdot)\) n/a 912 12
169.6.i \(\chi_{169}(3, \cdot)\) n/a 1776 24
169.6.k \(\chi_{169}(4, \cdot)\) n/a 1800 24

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(169))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(169)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)