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Properties

Label 84.3
Level 84
Weight 3
Dimension 150
Nonzero newspaces 8
Newform subspaces 18
Sturm bound 1152
Trace bound 1

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Defining parameters

Level: \( N \) = \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 18 \)
Sturm bound: \(1152\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(84))\).

Total New Old
Modular forms 444 174 270
Cusp forms 324 150 174
Eisenstein series 120 24 96

Trace form

\( 150 q + 4 q^{2} + 3 q^{3} + 2 q^{4} + 2 q^{5} - 12 q^{6} + 6 q^{7} - 2 q^{8} + 15 q^{9} + O(q^{10}) \) \( 150 q + 4 q^{2} + 3 q^{3} + 2 q^{4} + 2 q^{5} - 12 q^{6} + 6 q^{7} - 2 q^{8} + 15 q^{9} + 40 q^{10} + 54 q^{11} + 36 q^{12} + 50 q^{13} + 6 q^{15} - 46 q^{16} - 88 q^{17} - 90 q^{18} - 92 q^{19} - 268 q^{20} + 3 q^{21} - 264 q^{22} + 48 q^{23} - 84 q^{24} + 40 q^{25} - 22 q^{26} - 72 q^{27} - 6 q^{28} - 52 q^{29} + 6 q^{30} - 8 q^{31} + 214 q^{32} - 177 q^{33} + 292 q^{34} - 78 q^{35} - 126 q^{36} - 482 q^{37} + 54 q^{38} - 180 q^{39} + 208 q^{40} - 232 q^{41} - 54 q^{42} + 12 q^{43} - 168 q^{44} + 87 q^{45} - 84 q^{46} + 66 q^{47} - 96 q^{48} + 12 q^{49} - 294 q^{50} + 315 q^{51} - 56 q^{52} + 332 q^{53} + 198 q^{54} + 504 q^{55} + 354 q^{56} + 642 q^{57} + 568 q^{58} + 372 q^{59} + 504 q^{60} + 212 q^{61} + 708 q^{62} - 105 q^{63} + 470 q^{64} + 82 q^{65} + 522 q^{66} - 376 q^{67} + 536 q^{68} - 570 q^{69} + 216 q^{70} - 168 q^{71} + 594 q^{72} - 214 q^{73} - 226 q^{74} - 462 q^{75} - 216 q^{76} - 600 q^{77} + 72 q^{78} - 508 q^{79} - 352 q^{80} - 33 q^{81} - 128 q^{82} + 60 q^{84} + 284 q^{85} + 390 q^{86} + 468 q^{87} + 204 q^{88} - 4 q^{89} + 24 q^{90} + 484 q^{91} - 48 q^{92} + 513 q^{93} - 936 q^{94} + 330 q^{95} - 756 q^{96} - 712 q^{97} - 530 q^{98} + 102 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(84))\)

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
84.3.c \(\chi_{84}(29, \cdot)\) 84.3.c.a 4 1
84.3.d \(\chi_{84}(13, \cdot)\) 84.3.d.a 2 1
84.3.g \(\chi_{84}(43, \cdot)\) 84.3.g.a 12 1
84.3.h \(\chi_{84}(83, \cdot)\) 84.3.h.a 1 1
84.3.h.b 1
84.3.h.c 1
84.3.h.d 1
84.3.h.e 24
84.3.j \(\chi_{84}(47, \cdot)\) 84.3.j.a 56 2
84.3.l \(\chi_{84}(67, \cdot)\) 84.3.l.a 2 2
84.3.l.b 2
84.3.l.c 14
84.3.l.d 14
84.3.m \(\chi_{84}(61, \cdot)\) 84.3.m.a 2 2
84.3.m.b 4
84.3.p \(\chi_{84}(53, \cdot)\) 84.3.p.a 2 2
84.3.p.b 4
84.3.p.c 4

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(84))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(84)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)