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Properties

Label 171.12
Level 171
Weight 12
Dimension 9276
Nonzero newspaces 16
Sturm bound 25920
Trace bound 3

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Defining parameters

Level: \( N \) = \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) = \( 12 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(25920\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_1(171))\).

Total New Old
Modular forms 12024 9428 2596
Cusp forms 11736 9276 2460
Eisenstein series 288 152 136

Trace form

\( 9276 q + 147 q^{2} - 12 q^{3} + 11391 q^{4} + 13353 q^{5} - 41202 q^{6} - 160443 q^{7} + 537297 q^{8} - 271044 q^{9} + O(q^{10}) \) \( 9276 q + 147 q^{2} - 12 q^{3} + 11391 q^{4} + 13353 q^{5} - 41202 q^{6} - 160443 q^{7} + 537297 q^{8} - 271044 q^{9} - 1196625 q^{10} + 2570421 q^{11} - 2055756 q^{12} - 7343475 q^{13} + 15694341 q^{14} + 12717180 q^{15} - 11654457 q^{16} - 60195258 q^{17} - 17365788 q^{18} + 38203542 q^{19} - 82541982 q^{20} - 110024448 q^{21} - 25699785 q^{22} + 272402556 q^{23} + 422200674 q^{24} - 282797481 q^{25} - 1119989955 q^{26} + 167398668 q^{27} + 670876800 q^{28} - 209494509 q^{29} + 47165148 q^{30} + 165315339 q^{31} - 57706398 q^{32} - 62676720 q^{33} - 556697592 q^{34} - 69673263 q^{35} + 40006134 q^{36} + 589870560 q^{37} + 872265477 q^{38} + 3998129880 q^{39} - 1610403018 q^{40} - 309949077 q^{41} - 8343937800 q^{42} + 10707537438 q^{43} - 19420666800 q^{44} + 3632183658 q^{45} + 20481196848 q^{46} + 277658004 q^{47} - 16077239274 q^{48} - 7265911200 q^{49} + 24117959118 q^{50} + 19799613270 q^{51} + 61665060129 q^{52} + 4719948705 q^{53} - 39718133334 q^{54} - 41202052581 q^{55} - 134537036892 q^{56} - 32621476170 q^{57} + 26854709250 q^{58} + 98592677160 q^{59} + 188177514372 q^{60} + 127393528035 q^{61} - 145645525722 q^{62} - 127488597228 q^{63} - 257128404573 q^{64} - 81536866152 q^{65} + 64604341512 q^{66} + 159790369248 q^{67} + 569505111300 q^{68} + 107685115218 q^{69} - 312577815363 q^{70} - 595064183022 q^{71} - 499911805818 q^{72} + 204097411803 q^{73} + 459877183845 q^{74} + 436766088660 q^{75} + 274119016326 q^{76} + 163333209093 q^{77} - 300639741264 q^{78} - 317486269041 q^{79} - 1329808562787 q^{80} - 444614208660 q^{81} - 189994235934 q^{82} + 290070923466 q^{83} + 1423936031592 q^{84} + 1000740050505 q^{85} + 597568250094 q^{86} - 199430982468 q^{87} - 966711183609 q^{88} - 1645754033826 q^{89} - 1239164581554 q^{90} - 497330656485 q^{91} + 1720669787232 q^{92} + 1145962968672 q^{93} + 2222651152920 q^{94} - 1270961819634 q^{95} - 1484554649832 q^{96} - 18178658208 q^{97} + 972991877508 q^{98} - 118109642958 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_1(171))\)

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
171.12.a \(\chi_{171}(1, \cdot)\) 171.12.a.a 7 1
171.12.a.b 7
171.12.a.c 8
171.12.a.d 9
171.12.a.e 9
171.12.a.f 10
171.12.a.g 14
171.12.a.h 18
171.12.d \(\chi_{171}(170, \cdot)\) 171.12.d.a 4 1
171.12.d.b 68
171.12.e \(\chi_{171}(58, \cdot)\) n/a 396 2
171.12.f \(\chi_{171}(64, \cdot)\) n/a 180 2
171.12.g \(\chi_{171}(106, \cdot)\) n/a 436 2
171.12.h \(\chi_{171}(7, \cdot)\) n/a 436 2
171.12.k \(\chi_{171}(50, \cdot)\) n/a 436 2
171.12.l \(\chi_{171}(56, \cdot)\) n/a 436 2
171.12.m \(\chi_{171}(8, \cdot)\) n/a 144 2
171.12.t \(\chi_{171}(122, \cdot)\) n/a 436 2
171.12.u \(\chi_{171}(28, \cdot)\) n/a 546 6
171.12.v \(\chi_{171}(25, \cdot)\) n/a 1308 6
171.12.w \(\chi_{171}(4, \cdot)\) n/a 1308 6
171.12.x \(\chi_{171}(14, \cdot)\) n/a 1308 6
171.12.y \(\chi_{171}(53, \cdot)\) n/a 444 6
171.12.bd \(\chi_{171}(2, \cdot)\) n/a 1308 6

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

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_1(171))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_1(171)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 1}\)