Properties

Label 668.2
Level 668
Weight 2
Dimension 7968
Nonzero newspaces 4
Newforms 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: \( 4 \)
Newforms: \( 7 \)
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

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

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

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