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Properties

Label 189.4
Level 189
Weight 4
Dimension 2864
Nonzero newspaces 16
Newform subspaces 42
Sturm bound 10368
Trace bound 9

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Defining parameters

Level: \( N \) = \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 16 \)
Newform subspaces: \( 42 \)
Sturm bound: \(10368\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(189))\).

Total New Old
Modular forms 4068 3024 1044
Cusp forms 3708 2864 844
Eisenstein series 360 160 200

Trace form

\( 2864 q - 18 q^{2} - 24 q^{3} - 64 q^{4} - 66 q^{5} - q^{7} + 234 q^{8} + 72 q^{9} + O(q^{10}) \) \( 2864 q - 18 q^{2} - 24 q^{3} - 64 q^{4} - 66 q^{5} - q^{7} + 234 q^{8} + 72 q^{9} + 48 q^{10} - 270 q^{11} - 330 q^{12} - 320 q^{13} - 399 q^{14} + 368 q^{16} + 930 q^{17} + 1242 q^{18} + 400 q^{19} + 1908 q^{20} + 102 q^{21} + 294 q^{22} - 642 q^{23} - 2376 q^{24} - 892 q^{25} - 5196 q^{26} - 2286 q^{27} - 1306 q^{28} - 1530 q^{29} - 954 q^{30} - 176 q^{31} + 264 q^{32} + 1242 q^{33} - 564 q^{34} + 1203 q^{35} + 4104 q^{36} + 2056 q^{37} + 5886 q^{38} + 1500 q^{39} + 3636 q^{40} + 5136 q^{41} + 3042 q^{42} + 502 q^{43} + 5736 q^{44} + 684 q^{45} - 528 q^{46} - 2394 q^{47} - 726 q^{48} + 2891 q^{49} + 1512 q^{50} - 1566 q^{51} + 1780 q^{52} - 3264 q^{53} - 9864 q^{54} - 2796 q^{55} - 14055 q^{56} - 9228 q^{57} - 8880 q^{58} - 13596 q^{59} - 14760 q^{60} - 4304 q^{61} - 10182 q^{62} - 5238 q^{63} - 7126 q^{64} + 1116 q^{65} + 14994 q^{66} + 2392 q^{67} + 4650 q^{68} + 10440 q^{69} - 1401 q^{70} + 9330 q^{71} + 5076 q^{72} + 1948 q^{73} + 3270 q^{74} + 3216 q^{75} + 1384 q^{76} + 11691 q^{77} + 612 q^{78} + 844 q^{79} + 3690 q^{80} - 6912 q^{81} + 3564 q^{82} - 2616 q^{83} - 7710 q^{84} - 5898 q^{85} - 1926 q^{86} - 5796 q^{87} - 5880 q^{88} + 9168 q^{89} + 24984 q^{90} + 1255 q^{91} + 35754 q^{92} + 23568 q^{93} + 15816 q^{94} + 17610 q^{95} + 28152 q^{96} + 6700 q^{97} - 4512 q^{98} + 2412 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(189))\)

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
189.4.a \(\chi_{189}(1, \cdot)\) 189.4.a.a 1 1
189.4.a.b 1
189.4.a.c 1
189.4.a.d 1
189.4.a.e 2
189.4.a.f 2
189.4.a.g 2
189.4.a.h 2
189.4.a.i 2
189.4.a.j 3
189.4.a.k 3
189.4.a.l 4
189.4.c \(\chi_{189}(188, \cdot)\) 189.4.c.a 16 1
189.4.c.b 16
189.4.e \(\chi_{189}(109, \cdot)\) 189.4.e.a 2 2
189.4.e.b 2
189.4.e.c 2
189.4.e.d 2
189.4.e.e 12
189.4.e.f 14
189.4.e.g 14
189.4.e.h 16
189.4.f \(\chi_{189}(64, \cdot)\) 189.4.f.a 2 2
189.4.f.b 16
189.4.f.c 18
189.4.g \(\chi_{189}(100, \cdot)\) 189.4.g.a 44 2
189.4.h \(\chi_{189}(37, \cdot)\) 189.4.h.a 44 2
189.4.i \(\chi_{189}(143, \cdot)\) 189.4.i.a 44 2
189.4.o \(\chi_{189}(62, \cdot)\) 189.4.o.a 44 2
189.4.p \(\chi_{189}(26, \cdot)\) 189.4.p.a 2 2
189.4.p.b 2
189.4.p.c 12
189.4.p.d 16
189.4.p.e 32
189.4.s \(\chi_{189}(17, \cdot)\) 189.4.s.a 44 2
189.4.u \(\chi_{189}(4, \cdot)\) 189.4.u.a 420 6
189.4.v \(\chi_{189}(22, \cdot)\) 189.4.v.a 162 6
189.4.v.b 162
189.4.w \(\chi_{189}(25, \cdot)\) 189.4.w.a 420 6
189.4.ba \(\chi_{189}(5, \cdot)\) 189.4.ba.a 420 6
189.4.bd \(\chi_{189}(47, \cdot)\) 189.4.bd.a 420 6
189.4.be \(\chi_{189}(20, \cdot)\) 189.4.be.a 420 6

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(189))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(189)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 1}\)