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Properties

Label 183.2
Level 183
Weight 2
Dimension 869
Nonzero newspaces 12
Newform subspaces 32
Sturm bound 4960
Trace bound 1

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Defining parameters

Level: \( N \) = \( 183 = 3 \cdot 61 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Newform subspaces: \( 32 \)
Sturm bound: \(4960\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(183))\).

Total New Old
Modular forms 1360 989 371
Cusp forms 1121 869 252
Eisenstein series 239 120 119

Trace form

\( 869 q - 3 q^{2} - 31 q^{3} - 67 q^{4} - 6 q^{5} - 33 q^{6} - 68 q^{7} - 15 q^{8} - 31 q^{9} + O(q^{10}) \) \( 869 q - 3 q^{2} - 31 q^{3} - 67 q^{4} - 6 q^{5} - 33 q^{6} - 68 q^{7} - 15 q^{8} - 31 q^{9} - 78 q^{10} - 12 q^{11} - 37 q^{12} - 74 q^{13} - 24 q^{14} - 36 q^{15} - 91 q^{16} - 18 q^{17} - 33 q^{18} - 80 q^{19} - 42 q^{20} - 38 q^{21} - 96 q^{22} - 24 q^{23} - 45 q^{24} - 91 q^{25} - 42 q^{26} - 31 q^{27} - 116 q^{28} - 30 q^{29} - 48 q^{30} - 92 q^{31} - 63 q^{32} - 42 q^{33} - 114 q^{34} - 48 q^{35} - 37 q^{36} - 98 q^{37} - 60 q^{38} - 44 q^{39} - 150 q^{40} - 42 q^{41} - 54 q^{42} - 104 q^{43} - 84 q^{44} - 36 q^{45} - 132 q^{46} + 12 q^{47} + 39 q^{48} + 23 q^{49} + 57 q^{50} + 12 q^{51} + 292 q^{52} + 6 q^{53} - 33 q^{54} + 108 q^{55} + 240 q^{56} + 70 q^{57} + 90 q^{58} + 60 q^{59} + 198 q^{60} + 139 q^{61} + 264 q^{62} - 28 q^{63} + 293 q^{64} + 36 q^{65} + 54 q^{66} + 112 q^{67} + 234 q^{68} + 66 q^{69} + 156 q^{70} - 12 q^{71} + 45 q^{72} - 14 q^{73} + 36 q^{74} + 9 q^{75} - 36 q^{77} - 72 q^{78} - 140 q^{79} - 186 q^{80} - 31 q^{81} - 186 q^{82} - 84 q^{83} - 86 q^{84} - 168 q^{85} - 132 q^{86} - 60 q^{87} - 240 q^{88} - 90 q^{89} - 48 q^{90} - 172 q^{91} - 168 q^{92} - 62 q^{93} - 204 q^{94} - 120 q^{95} - 93 q^{96} - 158 q^{97} - 171 q^{98} - 42 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(183))\)

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
183.2.a \(\chi_{183}(1, \cdot)\) 183.2.a.a 2 1
183.2.a.b 3
183.2.a.c 6
183.2.c \(\chi_{183}(121, \cdot)\) 183.2.c.a 2 1
183.2.c.b 2
183.2.c.c 6
183.2.e \(\chi_{183}(13, \cdot)\) 183.2.e.a 2 2
183.2.e.b 4
183.2.e.c 4
183.2.e.d 6
183.2.e.e 6
183.2.g \(\chi_{183}(11, \cdot)\) 183.2.g.a 4 2
183.2.g.b 4
183.2.g.c 28
183.2.h \(\chi_{183}(34, \cdot)\) 183.2.h.a 20 4
183.2.h.b 28
183.2.j \(\chi_{183}(109, \cdot)\) 183.2.j.a 2 2
183.2.j.b 4
183.2.j.c 4
183.2.j.d 8
183.2.m \(\chi_{183}(52, \cdot)\) 183.2.m.a 16 4
183.2.m.b 24
183.2.o \(\chi_{183}(29, \cdot)\) 183.2.o.a 4 4
183.2.o.b 72
183.2.q \(\chi_{183}(16, \cdot)\) 183.2.q.a 40 8
183.2.q.b 48
183.2.r \(\chi_{183}(8, \cdot)\) 183.2.r.a 144 8
183.2.u \(\chi_{183}(4, \cdot)\) 183.2.u.a 16 8
183.2.u.b 16
183.2.u.c 40
183.2.x \(\chi_{183}(2, \cdot)\) 183.2.x.a 16 16
183.2.x.b 288

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(183))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(183)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(61))\)\(^{\oplus 2}\)