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Properties

Label 197.10
Level 197
Weight 10
Dimension 14455
Nonzero newspaces 6
Sturm bound 32340
Trace bound 1

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Defining parameters

Level: \( N \) = \( 197 \)
Weight: \( k \) = \( 10 \)
Nonzero newspaces: \( 6 \)
Sturm bound: \(32340\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(197))\).

Total New Old
Modular forms 14651 14649 2
Cusp forms 14455 14455 0
Eisenstein series 196 194 2

Trace form

\( 14455 q - 98 q^{2} - 98 q^{3} - 98 q^{4} - 98 q^{5} - 98 q^{6} - 98 q^{7} - 98 q^{8} - 98 q^{9} + O(q^{10}) \) \( 14455 q - 98 q^{2} - 98 q^{3} - 98 q^{4} - 98 q^{5} - 98 q^{6} - 98 q^{7} - 98 q^{8} - 98 q^{9} - 98 q^{10} - 98 q^{11} - 98 q^{12} - 98 q^{13} - 98 q^{14} - 98 q^{15} - 98 q^{16} - 98 q^{17} - 98 q^{18} - 98 q^{19} - 98 q^{20} - 98 q^{21} - 98 q^{22} - 98 q^{23} - 98 q^{24} - 98 q^{25} - 98 q^{26} - 98 q^{27} - 98 q^{28} - 98 q^{29} - 98 q^{30} - 98 q^{31} - 98 q^{32} - 98 q^{33} - 98 q^{34} - 98 q^{35} - 98 q^{36} - 98 q^{37} - 98 q^{38} - 98 q^{39} - 98 q^{40} - 98 q^{41} - 98 q^{42} - 98 q^{43} - 98 q^{44} - 98 q^{45} - 98 q^{46} - 98 q^{47} - 98 q^{48} - 98 q^{49} - 98 q^{50} - 98 q^{51} - 98 q^{52} - 98 q^{53} - 98 q^{54} - 98 q^{55} - 98 q^{56} - 98 q^{57} - 98 q^{58} - 98 q^{59} - 98 q^{60} - 98 q^{61} - 98 q^{62} - 98 q^{63} - 98 q^{64} - 98 q^{65} - 98 q^{66} - 98 q^{67} - 98 q^{68} - 98 q^{69} - 98 q^{70} - 98 q^{71} - 98 q^{72} - 98 q^{73} - 98 q^{74} - 98 q^{75} - 98 q^{76} - 98 q^{77} - 98 q^{78} - 98 q^{79} - 98 q^{80} - 98 q^{81} - 98 q^{82} - 98 q^{83} - 98 q^{84} - 98 q^{85} - 98 q^{86} - 98 q^{87} - 98 q^{88} - 98 q^{89} - 98 q^{90} - 98 q^{91} - 98 q^{92} - 98 q^{93} - 98 q^{94} - 98 q^{95} - 98 q^{96} - 98 q^{97} - 98 q^{98} - 98 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(197))\)

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
197.10.a \(\chi_{197}(1, \cdot)\) 197.10.a.a 71 1
197.10.a.b 76
197.10.b \(\chi_{197}(196, \cdot)\) n/a 148 1
197.10.d \(\chi_{197}(36, \cdot)\) n/a 882 6
197.10.e \(\chi_{197}(6, \cdot)\) n/a 888 6
197.10.g \(\chi_{197}(16, \cdot)\) n/a 6174 42
197.10.h \(\chi_{197}(4, \cdot)\) n/a 6216 42

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