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Properties

Label 66.4
Level 66
Weight 4
Dimension 88
Nonzero newspaces 4
Newform subspaces 11
Sturm bound 960
Trace bound 1

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Defining parameters

Level: \( N \) = \( 66 = 2 \cdot 3 \cdot 11 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 11 \)
Sturm bound: \(960\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(66))\).

Total New Old
Modular forms 400 88 312
Cusp forms 320 88 232
Eisenstein series 80 0 80

Trace form

\( 88 q + 4 q^{2} + 6 q^{3} - 8 q^{4} - 12 q^{5} - 62 q^{6} - 8 q^{7} + 16 q^{8} + 142 q^{9} + O(q^{10}) \) \( 88 q + 4 q^{2} + 6 q^{3} - 8 q^{4} - 12 q^{5} - 62 q^{6} - 8 q^{7} + 16 q^{8} + 142 q^{9} + 224 q^{10} + 188 q^{11} + 104 q^{12} + 4 q^{13} - 104 q^{14} - 374 q^{15} - 32 q^{16} - 368 q^{17} - 194 q^{18} + 410 q^{19} - 48 q^{20} + 324 q^{21} + 24 q^{22} + 44 q^{23} + 152 q^{24} + 538 q^{25} + 152 q^{26} - 6 q^{27} + 128 q^{28} - 760 q^{29} - 852 q^{30} - 1204 q^{31} + 64 q^{32} - 1899 q^{33} - 504 q^{34} - 388 q^{35} - 172 q^{36} - 508 q^{37} + 80 q^{38} + 988 q^{39} + 96 q^{40} + 656 q^{41} + 332 q^{42} - 2156 q^{43} - 1168 q^{44} + 1542 q^{45} - 48 q^{46} + 692 q^{47} + 96 q^{48} + 2834 q^{49} + 1004 q^{50} + 1389 q^{51} + 1616 q^{52} + 2724 q^{53} + 432 q^{54} + 2468 q^{55} - 256 q^{56} + 1625 q^{57} + 3480 q^{58} + 3360 q^{59} + 624 q^{60} - 1244 q^{61} - 3112 q^{62} - 5612 q^{63} - 128 q^{64} - 7176 q^{65} - 2992 q^{66} - 8448 q^{67} - 1472 q^{68} - 3232 q^{69} - 2064 q^{70} + 2096 q^{71} + 1264 q^{72} + 944 q^{73} + 3816 q^{74} + 6261 q^{75} + 1360 q^{76} + 4292 q^{77} + 2504 q^{78} + 5240 q^{79} + 1088 q^{80} + 11978 q^{81} + 7228 q^{82} + 3024 q^{83} + 2256 q^{84} + 10112 q^{85} - 1048 q^{86} + 180 q^{87} - 1024 q^{88} - 3120 q^{89} - 5324 q^{90} - 16524 q^{91} - 1344 q^{92} - 13558 q^{93} - 9664 q^{94} - 9600 q^{95} - 192 q^{96} - 10978 q^{97} - 348 q^{98} - 7998 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(66))\)

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
66.4.a \(\chi_{66}(1, \cdot)\) 66.4.a.a 1 1
66.4.a.b 1
66.4.a.c 2
66.4.b \(\chi_{66}(65, \cdot)\) 66.4.b.a 6 1
66.4.b.b 6
66.4.e \(\chi_{66}(25, \cdot)\) 66.4.e.a 4 4
66.4.e.b 4
66.4.e.c 8
66.4.e.d 8
66.4.h \(\chi_{66}(17, \cdot)\) 66.4.h.a 24 4
66.4.h.b 24

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(66))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(66)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)