↑

Properties

Label 169.12
Level 169
Weight 12
Dimension 12758
Nonzero newspaces 8
Sturm bound 28392
Trace bound 2

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 169 = 13^{2} \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(28392\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(169))\).

Total New Old
Modular forms 13127 12963 164
Cusp forms 12899 12758 141
Eisenstein series 228 205 23

Trace form

\( 12758 q - 90 q^{2} + 186 q^{3} - 1538 q^{4} + 4764 q^{5} - 6114 q^{6} - 120038 q^{7} + 674238 q^{8} - 1058493 q^{9} + O(q^{10}) \) \( 12758 q - 90 q^{2} + 186 q^{3} - 1538 q^{4} + 4764 q^{5} - 6114 q^{6} - 120038 q^{7} + 674238 q^{8} - 1058493 q^{9} + 2799534 q^{10} + 717774 q^{11} - 10324278 q^{12} - 181956 q^{13} + 13613634 q^{14} + 7766430 q^{15} - 40955970 q^{16} - 5334402 q^{17} + 97750338 q^{18} + 94496146 q^{19} - 306196434 q^{20} + 15691194 q^{21} + 282562866 q^{22} + 125121534 q^{23} - 310261986 q^{24} - 318468029 q^{25} - 168696102 q^{26} + 485459298 q^{27} + 678427210 q^{28} + 563144070 q^{29} + 270598686 q^{30} - 1247153390 q^{31} - 4284625734 q^{32} + 1280094426 q^{33} + 5229939294 q^{34} + 2821635954 q^{35} - 3602693706 q^{36} + 1069451506 q^{37} - 5960806230 q^{38} - 1250744808 q^{39} - 3499528014 q^{40} + 12287096262 q^{41} + 16789551162 q^{42} - 5309008770 q^{43} - 19989970326 q^{44} - 20158970226 q^{45} + 3964970214 q^{46} + 14364990402 q^{47} + 41293282590 q^{48} + 9565761427 q^{49} - 14445294774 q^{50} - 74841263790 q^{51} - 6451520714 q^{52} + 12050843952 q^{53} + 50654808930 q^{54} + 37912778586 q^{55} + 3760917546 q^{56} - 7539198342 q^{57} - 29713433202 q^{58} - 20233526202 q^{59} + 11948556018 q^{60} - 2965884430 q^{61} + 8555598078 q^{62} - 43426178790 q^{63} + 47592996058 q^{64} + 13129921827 q^{65} - 109041755814 q^{66} + 38610615658 q^{67} - 138267987030 q^{68} + 45677303154 q^{69} + 74469887562 q^{70} + 130374830094 q^{71} + 106711060122 q^{72} + 163940935120 q^{73} - 111448193082 q^{74} - 208750571562 q^{75} + 41754439318 q^{76} + 12366337890 q^{77} - 97637655234 q^{78} - 109877076502 q^{79} - 437047470846 q^{80} - 43351787745 q^{81} + 518559790230 q^{82} + 453818970678 q^{83} + 760450395354 q^{84} + 438274481040 q^{85} - 1021742535870 q^{86} - 693680610858 q^{87} - 639719994006 q^{88} + 195334346856 q^{89} + 402645796674 q^{90} - 69864453854 q^{91} + 328723745538 q^{92} - 875097738174 q^{93} - 680977506954 q^{94} - 417424223874 q^{95} + 2935878692826 q^{96} + 1242031043488 q^{97} + 40967223246 q^{98} + 565594016670 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(169))\)

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
169.12.a \(\chi_{169}(1, \cdot)\) 169.12.a.a 1 1
169.12.a.b 5
169.12.a.c 6
169.12.a.d 12
169.12.a.e 12
169.12.a.f 12
169.12.a.g 22
169.12.a.h 33
169.12.a.i 33
169.12.b \(\chi_{169}(168, \cdot)\) n/a 136 1
169.12.c \(\chi_{169}(22, \cdot)\) n/a 272 2
169.12.e \(\chi_{169}(23, \cdot)\) n/a 274 2
169.12.g \(\chi_{169}(14, \cdot)\) n/a 2004 12
169.12.h \(\chi_{169}(12, \cdot)\) n/a 1992 12
169.12.i \(\chi_{169}(3, \cdot)\) n/a 3984 24
169.12.k \(\chi_{169}(4, \cdot)\) n/a 3960 24

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

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(169))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(169)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)