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Properties

Label 84.7
Level 84
Weight 7
Dimension 476
Nonzero newspaces 8
Newform subspaces 16
Sturm bound 2688
Trace bound 1

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Defining parameters

Level: \( N \) = \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) = \( 7 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 16 \)
Sturm bound: \(2688\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(84))\).

Total New Old
Modular forms 1212 500 712
Cusp forms 1092 476 616
Eisenstein series 120 24 96

Trace form

\( 476 q + 20 q^{2} + 12 q^{3} - 318 q^{4} - 248 q^{5} + 324 q^{6} + 476 q^{7} - 1762 q^{8} + 3906 q^{9} + O(q^{10}) \) \( 476 q + 20 q^{2} + 12 q^{3} - 318 q^{4} - 248 q^{5} + 324 q^{6} + 476 q^{7} - 1762 q^{8} + 3906 q^{9} + 960 q^{10} + 1512 q^{11} + 7716 q^{12} + 1264 q^{13} - 17568 q^{14} + 456 q^{15} - 174 q^{16} - 26120 q^{17} + 10362 q^{18} + 12640 q^{19} + 45172 q^{20} - 36078 q^{21} - 2328 q^{22} + 17808 q^{23} - 37668 q^{24} + 17540 q^{25} + 60754 q^{26} + 62892 q^{27} + 125370 q^{28} - 44360 q^{29} - 39294 q^{30} - 58664 q^{31} - 48010 q^{32} - 121626 q^{33} - 419148 q^{34} + 177792 q^{35} - 126750 q^{36} + 419836 q^{37} + 371214 q^{38} + 12852 q^{39} + 484848 q^{40} + 130504 q^{41} - 181446 q^{42} - 733544 q^{43} - 666408 q^{44} + 134742 q^{45} + 376404 q^{46} + 189168 q^{47} + 552096 q^{48} + 29324 q^{49} + 829986 q^{50} + 288828 q^{51} - 640248 q^{52} - 897776 q^{53} - 279954 q^{54} - 172296 q^{55} - 372702 q^{56} + 359988 q^{57} - 1803624 q^{58} - 1215984 q^{59} + 2040024 q^{60} - 596276 q^{61} + 2373204 q^{62} + 583584 q^{63} + 2916246 q^{64} + 1041512 q^{65} - 1635450 q^{66} + 823288 q^{67} - 1861640 q^{68} - 2514600 q^{69} - 1399824 q^{70} - 1709904 q^{71} - 1055454 q^{72} + 491956 q^{73} - 139658 q^{74} - 811332 q^{75} - 2571480 q^{76} + 2511456 q^{77} + 1962312 q^{78} + 3054136 q^{79} + 3487168 q^{80} - 3154434 q^{81} + 3392592 q^{82} - 2637204 q^{84} - 3239496 q^{85} - 2473698 q^{86} - 3174444 q^{87} - 1791156 q^{88} - 2272280 q^{89} + 40824 q^{90} - 490232 q^{91} + 7638672 q^{92} + 678246 q^{93} + 3704400 q^{94} + 6943440 q^{95} + 8541420 q^{96} + 1783864 q^{97} + 2029958 q^{98} - 2263776 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(84))\)

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
84.7.c \(\chi_{84}(29, \cdot)\) 84.7.c.a 12 1
84.7.d \(\chi_{84}(13, \cdot)\) 84.7.d.a 8 1
84.7.g \(\chi_{84}(43, \cdot)\) 84.7.g.a 36 1
84.7.h \(\chi_{84}(83, \cdot)\) 84.7.h.a 1 1
84.7.h.b 1
84.7.h.c 1
84.7.h.d 1
84.7.h.e 88
84.7.j \(\chi_{84}(47, \cdot)\) 84.7.j.a 184 2
84.7.l \(\chi_{84}(67, \cdot)\) 84.7.l.a 48 2
84.7.l.b 48
84.7.m \(\chi_{84}(61, \cdot)\) 84.7.m.a 8 2
84.7.m.b 8
84.7.p \(\chi_{84}(53, \cdot)\) 84.7.p.a 2 2
84.7.p.b 2
84.7.p.c 28

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(84))\) into lower level spaces

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