Properties

Label 668.2
Level 668
Weight 2
Dimension 7968
Nonzero newspaces 4
Newform subspaces 7
Sturm bound 55776
Trace bound 1

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Defining parameters

Level: \( N \) = \( 668 = 2^{2} \cdot 167 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 7 \)
Sturm bound: \(55776\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(668))\).

Total New Old
Modular forms 14359 8300 6059
Cusp forms 13530 7968 5562
Eisenstein series 829 332 497

Trace form

\( 7968q - 83q^{2} - 83q^{4} - 166q^{5} - 83q^{6} - 83q^{8} - 166q^{9} + O(q^{10}) \) \( 7968q - 83q^{2} - 83q^{4} - 166q^{5} - 83q^{6} - 83q^{8} - 166q^{9} - 83q^{10} - 83q^{12} - 166q^{13} - 83q^{14} - 83q^{16} - 166q^{17} - 83q^{18} - 83q^{20} - 166q^{21} - 83q^{22} - 83q^{24} - 166q^{25} - 83q^{26} - 83q^{28} - 166q^{29} - 83q^{30} - 83q^{32} - 166q^{33} - 83q^{34} - 83q^{36} - 166q^{37} - 83q^{38} - 83q^{40} - 166q^{41} - 83q^{42} - 83q^{44} - 166q^{45} - 83q^{46} - 83q^{48} - 166q^{49} - 83q^{50} - 83q^{52} - 166q^{53} - 83q^{54} - 83q^{56} - 166q^{57} - 83q^{58} - 83q^{60} - 166q^{61} - 83q^{62} - 83q^{64} - 166q^{65} - 83q^{66} - 83q^{68} - 166q^{69} - 83q^{70} - 83q^{72} - 166q^{73} - 83q^{74} - 83q^{76} - 166q^{77} - 83q^{78} - 83q^{80} - 166q^{81} - 83q^{82} - 83q^{84} - 166q^{85} - 83q^{86} - 83q^{88} - 166q^{89} - 83q^{90} - 83q^{92} - 166q^{93} - 83q^{94} - 83q^{96} - 166q^{97} - 83q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(668))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
668.2.a \(\chi_{668}(1, \cdot)\) 668.2.a.a 2 1
668.2.a.b 5
668.2.a.c 7
668.2.b \(\chi_{668}(667, \cdot)\) 668.2.b.a 22 1
668.2.b.b 60
668.2.e \(\chi_{668}(9, \cdot)\) 668.2.e.a 1148 82
668.2.h \(\chi_{668}(15, \cdot)\) 668.2.h.a 6724 82

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(668))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(668)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(334))\)\(^{\oplus 2}\)