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Properties

Label 211.2
Level 211
Weight 2
Dimension 1751
Nonzero newspaces 8
Newform subspaces 12
Sturm bound 7420
Trace bound 1

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Defining parameters

Level: \( N \) = \( 211 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 12 \)
Sturm bound: \(7420\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(211))\).

Total New Old
Modular forms 1960 1960 0
Cusp forms 1751 1751 0
Eisenstein series 209 209 0

Trace form

\( 1751 q - 102 q^{2} - 101 q^{3} - 98 q^{4} - 99 q^{5} - 93 q^{6} - 97 q^{7} - 90 q^{8} - 92 q^{9} + O(q^{10}) \) \( 1751 q - 102 q^{2} - 101 q^{3} - 98 q^{4} - 99 q^{5} - 93 q^{6} - 97 q^{7} - 90 q^{8} - 92 q^{9} - 87 q^{10} - 93 q^{11} - 77 q^{12} - 91 q^{13} - 81 q^{14} - 81 q^{15} - 74 q^{16} - 87 q^{17} - 66 q^{18} - 85 q^{19} - 63 q^{20} - 73 q^{21} - 69 q^{22} - 81 q^{23} - 45 q^{24} - 74 q^{25} - 63 q^{26} - 65 q^{27} - 49 q^{28} - 75 q^{29} - 33 q^{30} - 73 q^{31} - 42 q^{32} - 57 q^{33} - 51 q^{34} - 57 q^{35} - 14 q^{36} - 67 q^{37} - 45 q^{38} - 49 q^{39} - 15 q^{40} - 63 q^{41} - 9 q^{42} - 61 q^{43} - 21 q^{44} - 27 q^{45} - 33 q^{46} - 57 q^{47} + 19 q^{48} - 48 q^{49} - 12 q^{50} - 33 q^{51} - 7 q^{52} - 51 q^{53} + 15 q^{54} - 33 q^{55} + 15 q^{56} - 25 q^{57} - 15 q^{58} - 45 q^{59} + 63 q^{60} - 43 q^{61} - 9 q^{62} - q^{63} + 22 q^{64} - 21 q^{65} + 39 q^{66} - 37 q^{67} + 21 q^{68} - 9 q^{69} + 39 q^{70} - 33 q^{71} + 90 q^{72} - 31 q^{73} + 9 q^{74} + 19 q^{75} + 35 q^{76} - 9 q^{77} + 63 q^{78} - 25 q^{79} + 81 q^{80} + 16 q^{81} + 21 q^{82} - 21 q^{83} + 119 q^{84} + 3 q^{85} + 27 q^{86} + 15 q^{87} + 75 q^{88} - 15 q^{89} + 129 q^{90} + 7 q^{91} + 63 q^{92} + 23 q^{93} + 39 q^{94} + 15 q^{95} + 147 q^{96} - 7 q^{97} + 66 q^{98} + 51 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(211))\)

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
211.2.a \(\chi_{211}(1, \cdot)\) 211.2.a.a 2 1
211.2.a.b 3
211.2.a.c 3
211.2.a.d 9
211.2.c \(\chi_{211}(14, \cdot)\) 211.2.c.a 34 2
211.2.d \(\chi_{211}(55, \cdot)\) 211.2.d.a 4 4
211.2.d.b 60
211.2.f \(\chi_{211}(58, \cdot)\) 211.2.f.a 96 6
211.2.i \(\chi_{211}(19, \cdot)\) 211.2.i.a 136 8
211.2.j \(\chi_{211}(34, \cdot)\) 211.2.j.a 204 12
211.2.l \(\chi_{211}(5, \cdot)\) 211.2.l.a 384 24
211.2.o \(\chi_{211}(4, \cdot)\) 211.2.o.a 816 48