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Properties

Label 180.3
Level 180
Weight 3
Dimension 706
Nonzero newspaces 12
Newform subspaces 28
Sturm bound 5184
Trace bound 7

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Defining parameters

Level: \( N \) = \( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 28 \)
Sturm bound: \(5184\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(180))\).

Total New Old
Modular forms 1888 758 1130
Cusp forms 1568 706 862
Eisenstein series 320 52 268

Trace form

\( 706 q - 8 q^{2} - 6 q^{3} - 14 q^{4} - 29 q^{5} + 2 q^{6} - 12 q^{7} + 64 q^{8} - 6 q^{9} + O(q^{10}) \) \( 706 q - 8 q^{2} - 6 q^{3} - 14 q^{4} - 29 q^{5} + 2 q^{6} - 12 q^{7} + 64 q^{8} - 6 q^{9} + 14 q^{10} + 44 q^{11} + 64 q^{12} + 4 q^{13} + 60 q^{14} + 57 q^{15} + 10 q^{16} + 146 q^{17} - 16 q^{18} + 76 q^{19} + 36 q^{20} - 50 q^{21} + 110 q^{22} + 20 q^{23} - 126 q^{24} + 25 q^{25} - 252 q^{26} + 48 q^{27} - 16 q^{28} + 114 q^{29} - 204 q^{30} - 78 q^{31} - 418 q^{32} + 132 q^{33} - 234 q^{34} - 82 q^{35} - 150 q^{36} - 54 q^{37} - 10 q^{38} - 74 q^{39} - 224 q^{40} - 60 q^{41} + 520 q^{42} + 46 q^{43} + 340 q^{44} + 141 q^{45} + 8 q^{46} + 216 q^{47} + 314 q^{48} + 318 q^{49} - 334 q^{50} - 42 q^{51} - 376 q^{52} - 274 q^{53} - 382 q^{54} + 242 q^{55} - 740 q^{56} - 742 q^{57} - 632 q^{58} - 432 q^{59} - 524 q^{60} - 642 q^{61} - 836 q^{62} - 598 q^{63} - 116 q^{64} - 1019 q^{65} - 644 q^{66} - 726 q^{67} - 10 q^{68} - 806 q^{69} + 846 q^{70} - 428 q^{71} + 378 q^{72} - 706 q^{73} + 924 q^{74} - 471 q^{75} + 886 q^{76} + 358 q^{77} + 356 q^{78} + 394 q^{79} + 392 q^{80} + 390 q^{81} + 904 q^{82} + 300 q^{83} + 580 q^{84} + 596 q^{85} + 558 q^{86} + 22 q^{87} + 86 q^{88} + 568 q^{89} - 36 q^{90} + 416 q^{91} - 492 q^{92} + 1354 q^{93} - 1084 q^{94} - 128 q^{95} - 808 q^{96} + 38 q^{97} - 1626 q^{98} + 298 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(180))\)

We only show spaces with odd 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
180.3.b \(\chi_{180}(89, \cdot)\) 180.3.b.a 4 1
180.3.c \(\chi_{180}(91, \cdot)\) 180.3.c.a 4 1
180.3.c.b 8
180.3.c.c 8
180.3.f \(\chi_{180}(19, \cdot)\) 180.3.f.a 1 1
180.3.f.b 1
180.3.f.c 2
180.3.f.d 4
180.3.f.e 4
180.3.f.f 4
180.3.f.g 4
180.3.f.h 8
180.3.g \(\chi_{180}(161, \cdot)\) 180.3.g.a 4 1
180.3.l \(\chi_{180}(37, \cdot)\) 180.3.l.a 2 2
180.3.l.b 4
180.3.l.c 4
180.3.m \(\chi_{180}(107, \cdot)\) 180.3.m.a 4 2
180.3.m.b 4
180.3.m.c 40
180.3.o \(\chi_{180}(41, \cdot)\) 180.3.o.a 4 2
180.3.o.b 12
180.3.p \(\chi_{180}(79, \cdot)\) 180.3.p.a 4 2
180.3.p.b 4
180.3.p.c 128
180.3.s \(\chi_{180}(31, \cdot)\) 180.3.s.a 96 2
180.3.t \(\chi_{180}(29, \cdot)\) 180.3.t.a 24 2
180.3.u \(\chi_{180}(13, \cdot)\) 180.3.u.a 48 4
180.3.v \(\chi_{180}(23, \cdot)\) 180.3.v.a 272 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(180))\) into lower level spaces

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