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Properties

Label 236.2
Level 236
Weight 2
Dimension 957
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 6960
Trace bound 1

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Defining parameters

Level: \( N \) = \( 236 = 2^{2} \cdot 59 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(6960\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(236))\).

Total New Old
Modular forms 1885 1073 812
Cusp forms 1596 957 639
Eisenstein series 289 116 173

Trace form

\( 957 q - 29 q^{2} - 29 q^{4} - 58 q^{5} - 29 q^{6} - 29 q^{8} - 58 q^{9} + O(q^{10}) \) \( 957 q - 29 q^{2} - 29 q^{4} - 58 q^{5} - 29 q^{6} - 29 q^{8} - 58 q^{9} - 29 q^{10} - 29 q^{12} - 58 q^{13} - 29 q^{14} - 29 q^{16} - 58 q^{17} - 29 q^{18} - 29 q^{20} - 58 q^{21} - 29 q^{22} - 29 q^{24} - 58 q^{25} - 29 q^{26} - 29 q^{28} - 58 q^{29} - 29 q^{30} - 29 q^{32} - 58 q^{33} - 29 q^{34} - 29 q^{36} - 58 q^{37} - 29 q^{38} - 29 q^{40} - 58 q^{41} - 29 q^{42} - 29 q^{44} - 87 q^{45} - 29 q^{46} - 29 q^{47} - 29 q^{48} - 116 q^{49} - 29 q^{50} - 116 q^{51} - 29 q^{52} - 116 q^{53} - 29 q^{54} - 87 q^{55} - 29 q^{56} - 203 q^{57} - 58 q^{59} - 58 q^{60} - 116 q^{61} - 29 q^{62} - 145 q^{63} - 29 q^{64} - 145 q^{65} - 29 q^{66} - 58 q^{67} - 29 q^{68} - 174 q^{69} - 29 q^{70} - 58 q^{71} - 29 q^{72} - 87 q^{73} - 29 q^{74} - 29 q^{75} - 29 q^{76} - 58 q^{77} - 29 q^{78} - 29 q^{80} - 58 q^{81} - 29 q^{82} - 29 q^{84} - 58 q^{85} - 29 q^{86} - 29 q^{88} - 58 q^{89} - 29 q^{90} - 29 q^{92} - 58 q^{93} - 29 q^{94} - 29 q^{96} - 58 q^{97} + 58 q^{98} + 87 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(236))\)

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
236.2.a \(\chi_{236}(1, \cdot)\) 236.2.a.a 1 1
236.2.a.b 1
236.2.a.c 3
236.2.c \(\chi_{236}(235, \cdot)\) 236.2.c.a 28 1
236.2.e \(\chi_{236}(5, \cdot)\) 236.2.e.a 140 28
236.2.g \(\chi_{236}(11, \cdot)\) 236.2.g.a 784 28

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(236))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(236)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 2}\)