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Properties

Label 211.3
Level 211
Weight 3
Dimension 3605
Nonzero newspaces 8
Newform subspaces 9
Sturm bound 11130
Trace bound 1

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Defining parameters

Level: \( N \) = \( 211 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 9 \)
Sturm bound: \(11130\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(211))\).

Total New Old
Modular forms 3815 3815 0
Cusp forms 3605 3605 0
Eisenstein series 210 210 0

Trace form

\( 3605 q - 105 q^{2} - 105 q^{3} - 105 q^{4} - 105 q^{5} - 105 q^{6} - 105 q^{7} - 105 q^{8} - 105 q^{9} + O(q^{10}) \) \( 3605 q - 105 q^{2} - 105 q^{3} - 105 q^{4} - 105 q^{5} - 105 q^{6} - 105 q^{7} - 105 q^{8} - 105 q^{9} - 105 q^{10} - 105 q^{11} - 105 q^{12} - 105 q^{13} - 105 q^{14} - 105 q^{15} - 105 q^{16} - 105 q^{17} - 105 q^{18} - 105 q^{19} - 105 q^{20} - 105 q^{21} - 105 q^{22} - 105 q^{23} - 105 q^{24} - 105 q^{25} - 105 q^{26} - 105 q^{27} - 105 q^{28} - 105 q^{29} - 105 q^{30} - 105 q^{31} - 105 q^{32} - 105 q^{33} - 105 q^{34} - 105 q^{35} - 105 q^{36} - 105 q^{37} - 105 q^{38} - 105 q^{39} - 105 q^{40} - 105 q^{41} - 105 q^{42} - 105 q^{43} - 105 q^{44} - 105 q^{45} - 105 q^{46} - 105 q^{47} - 105 q^{48} - 105 q^{49} - 105 q^{50} - 105 q^{51} - 105 q^{52} - 105 q^{53} - 105 q^{54} - 105 q^{55} - 105 q^{56} - 105 q^{57} - 105 q^{58} - 105 q^{59} - 105 q^{60} - 105 q^{61} - 105 q^{62} - 105 q^{63} - 105 q^{64} - 105 q^{65} - 105 q^{66} - 105 q^{67} - 105 q^{68} - 105 q^{69} - 105 q^{70} - 105 q^{71} - 105 q^{72} - 105 q^{73} - 105 q^{74} - 105 q^{75} - 105 q^{76} - 105 q^{77} - 105 q^{78} - 105 q^{79} - 105 q^{80} - 105 q^{81} - 105 q^{82} - 105 q^{83} - 105 q^{84} - 105 q^{85} - 105 q^{86} - 105 q^{87} - 105 q^{88} - 105 q^{89} - 105 q^{90} - 105 q^{91} - 105 q^{92} - 105 q^{93} - 105 q^{94} - 105 q^{95} - 105 q^{96} - 105 q^{97} - 105 q^{98} - 105 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(211))\)

We only show spaces with odd 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
211.3.b \(\chi_{211}(210, \cdot)\) 211.3.b.a 3 1
211.3.b.b 32
211.3.e \(\chi_{211}(15, \cdot)\) 211.3.e.a 68 2
211.3.g \(\chi_{211}(23, \cdot)\) 211.3.g.a 140 4
211.3.h \(\chi_{211}(12, \cdot)\) 211.3.h.a 210 6
211.3.k \(\chi_{211}(10, \cdot)\) 211.3.k.a 272 8
211.3.m \(\chi_{211}(26, \cdot)\) 211.3.m.a 408 12
211.3.n \(\chi_{211}(8, \cdot)\) 211.3.n.a 840 24
211.3.p \(\chi_{211}(2, \cdot)\) 211.3.p.a 1632 48