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Properties

Label 1997.4
Level 1997
Weight 4
Dimension 497503
Nonzero newspaces 4
Sturm bound 1329336
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1997 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 4 \)
Sturm bound: \(1329336\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1997))\).

Total New Old
Modular forms 499499 499497 2
Cusp forms 497503 497503 0
Eisenstein series 1996 1994 2

Trace form

\( 497503 q - 998 q^{2} - 998 q^{3} - 998 q^{4} - 998 q^{5} - 998 q^{6} - 998 q^{7} - 998 q^{8} - 998 q^{9} + O(q^{10}) \) \( 497503 q - 998 q^{2} - 998 q^{3} - 998 q^{4} - 998 q^{5} - 998 q^{6} - 998 q^{7} - 998 q^{8} - 998 q^{9} - 998 q^{10} - 998 q^{11} - 998 q^{12} - 998 q^{13} - 998 q^{14} - 998 q^{15} - 998 q^{16} - 998 q^{17} - 998 q^{18} - 998 q^{19} - 998 q^{20} - 998 q^{21} - 998 q^{22} - 998 q^{23} - 998 q^{24} - 998 q^{25} - 998 q^{26} - 998 q^{27} - 998 q^{28} - 998 q^{29} - 998 q^{30} - 998 q^{31} - 998 q^{32} - 998 q^{33} - 998 q^{34} - 998 q^{35} - 998 q^{36} - 998 q^{37} - 998 q^{38} - 998 q^{39} - 998 q^{40} - 998 q^{41} - 998 q^{42} - 998 q^{43} - 998 q^{44} - 998 q^{45} - 998 q^{46} - 998 q^{47} - 998 q^{48} - 998 q^{49} - 998 q^{50} - 998 q^{51} - 998 q^{52} - 998 q^{53} - 998 q^{54} - 998 q^{55} - 998 q^{56} - 998 q^{57} - 998 q^{58} - 998 q^{59} - 998 q^{60} - 998 q^{61} - 998 q^{62} - 998 q^{63} - 998 q^{64} - 998 q^{65} - 998 q^{66} - 998 q^{67} - 998 q^{68} - 998 q^{69} - 998 q^{70} - 998 q^{71} - 998 q^{72} - 998 q^{73} - 998 q^{74} - 998 q^{75} - 998 q^{76} - 998 q^{77} - 998 q^{78} - 998 q^{79} - 998 q^{80} - 998 q^{81} - 998 q^{82} - 998 q^{83} - 998 q^{84} - 998 q^{85} - 998 q^{86} - 998 q^{87} - 998 q^{88} - 998 q^{89} - 998 q^{90} - 998 q^{91} - 998 q^{92} - 998 q^{93} - 998 q^{94} - 998 q^{95} - 998 q^{96} - 998 q^{97} - 998 q^{98} - 998 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1997))\)

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
1997.4.a \(\chi_{1997}(1, \cdot)\) 1997.4.a.a 239 1
1997.4.a.b 260
1997.4.b \(\chi_{1997}(1996, \cdot)\) n/a 498 1
1997.4.d \(\chi_{1997}(6, \cdot)\) n/a 248502 498
1997.4.e \(\chi_{1997}(4, \cdot)\) n/a 248004 498

"n/a" means that newforms for that character have not been added to the database yet