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Properties

Label 180.6
Level 180
Weight 6
Dimension 1803
Nonzero newspaces 12
Sturm bound 10368
Trace bound 4

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Defining parameters

Level: \( N \) = \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(10368\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(180))\).

Total New Old
Modular forms 4480 1859 2621
Cusp forms 4160 1803 2357
Eisenstein series 320 56 264

Trace form

\( 1803 q - 24 q^{3} + 38 q^{4} + 88 q^{5} + 38 q^{6} - 312 q^{7} + 240 q^{8} + 48 q^{9} + O(q^{10}) \) \( 1803 q - 24 q^{3} + 38 q^{4} + 88 q^{5} + 38 q^{6} - 312 q^{7} + 240 q^{8} + 48 q^{9} - 50 q^{10} - 394 q^{11} + 964 q^{12} + 10 q^{13} + 3024 q^{14} + 2055 q^{15} + 6306 q^{16} - 3136 q^{17} - 4120 q^{18} + 788 q^{19} - 8318 q^{20} - 6278 q^{21} - 11370 q^{22} + 12696 q^{23} + 12294 q^{24} + 39558 q^{25} + 3308 q^{26} + 4152 q^{27} + 11608 q^{28} + 14424 q^{29} - 25566 q^{30} + 838 q^{31} + 12790 q^{32} - 77574 q^{33} - 58782 q^{34} + 3320 q^{35} + 38226 q^{36} + 9048 q^{37} + 76670 q^{38} + 22966 q^{39} - 8442 q^{40} + 68200 q^{41} - 67268 q^{42} + 30932 q^{43} - 36525 q^{45} + 31864 q^{46} - 1404 q^{47} - 2530 q^{48} - 88767 q^{49} - 180944 q^{50} - 51864 q^{51} - 53120 q^{52} + 32432 q^{53} - 101650 q^{54} - 77466 q^{55} + 62596 q^{56} - 66064 q^{57} - 35072 q^{58} - 23254 q^{59} + 144322 q^{60} - 34960 q^{61} + 160460 q^{62} + 282506 q^{63} + 365372 q^{64} + 40021 q^{65} - 69260 q^{66} + 73956 q^{67} - 300002 q^{68} - 86666 q^{69} - 112392 q^{70} - 187500 q^{71} + 413658 q^{72} - 358312 q^{73} + 557484 q^{74} + 44997 q^{75} + 90910 q^{76} - 204894 q^{77} - 564664 q^{78} + 341366 q^{79} - 831568 q^{80} + 406812 q^{81} + 209052 q^{82} + 282876 q^{83} - 69260 q^{84} + 23886 q^{85} + 358094 q^{86} - 243014 q^{87} - 361434 q^{88} - 698594 q^{89} + 955026 q^{90} - 887792 q^{91} + 174016 q^{92} - 359510 q^{93} + 254620 q^{94} + 15216 q^{95} - 284344 q^{96} - 405834 q^{97} - 1484034 q^{98} + 698590 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(180))\)

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
180.6.a \(\chi_{180}(1, \cdot)\) 180.6.a.a 1 1
180.6.a.b 1
180.6.a.c 1
180.6.a.d 1
180.6.a.e 1
180.6.a.f 2
180.6.a.g 2
180.6.d \(\chi_{180}(109, \cdot)\) 180.6.d.a 2 1
180.6.d.b 2
180.6.d.c 2
180.6.d.d 6
180.6.e \(\chi_{180}(71, \cdot)\) 180.6.e.a 40 1
180.6.h \(\chi_{180}(179, \cdot)\) 180.6.h.a 4 1
180.6.h.b 56
180.6.i \(\chi_{180}(61, \cdot)\) 180.6.i.a 18 2
180.6.i.b 22
180.6.j \(\chi_{180}(17, \cdot)\) 180.6.j.a 20 2
180.6.k \(\chi_{180}(127, \cdot)\) n/a 146 2
180.6.n \(\chi_{180}(59, \cdot)\) n/a 352 2
180.6.q \(\chi_{180}(11, \cdot)\) n/a 240 2
180.6.r \(\chi_{180}(49, \cdot)\) 180.6.r.a 60 2
180.6.w \(\chi_{180}(77, \cdot)\) n/a 120 4
180.6.x \(\chi_{180}(7, \cdot)\) n/a 704 4

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(180))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(180)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)