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Properties

Label 3736.1
Level 3736
Weight 1
Dimension 246
Nonzero newspaces 3
Newform subspaces 4
Sturm bound 872352
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3736 = 2^{3} \cdot 467 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 4 \)
Sturm bound: \(872352\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3736))\).

Total New Old
Modular forms 3068 1176 1892
Cusp forms 272 246 26
Eisenstein series 2796 930 1866

The following table gives the dimensions of subspaces with specified projective image type.

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 244 0 2 0

Trace form

\( 246 q - q^{2} - 4 q^{3} + 11 q^{4} - 2 q^{6} - q^{8} + 9 q^{9} + O(q^{10}) \) \( 246 q - q^{2} - 4 q^{3} + 11 q^{4} - 2 q^{6} - q^{8} + 9 q^{9} - 2 q^{10} - 2 q^{11} - 2 q^{12} + 4 q^{13} + 11 q^{16} - 2 q^{17} - 3 q^{18} - 2 q^{19} - 2 q^{21} - 4 q^{22} - 4 q^{23} - 2 q^{24} + 7 q^{25} - 2 q^{27} - 2 q^{28} - q^{32} - 4 q^{33} - 2 q^{34} + 9 q^{36} - 4 q^{38} - 4 q^{39} - 2 q^{40} - 4 q^{41} - 2 q^{43} - 2 q^{44} - 2 q^{47} - 2 q^{48} + 9 q^{49} - q^{50} - 6 q^{51} + 2 q^{53} - 4 q^{54} - 8 q^{55} - 4 q^{57} - 2 q^{58} - 2 q^{63} + 11 q^{64} - 4 q^{66} - 2 q^{67} - 4 q^{68} + 2 q^{69} - 4 q^{70} - 2 q^{71} - 3 q^{72} - 2 q^{73} - 2 q^{74} - 2 q^{76} + 5 q^{81} - 2 q^{82} - 4 q^{83} - 2 q^{86} - 4 q^{88} - 8 q^{89} - 2 q^{90} + 4 q^{91} - 2 q^{92} - 8 q^{95} - 2 q^{96} - 2 q^{97} - q^{98} - 6 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3736))\)

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
3736.1.d \(\chi_{3736}(935, \cdot)\) None 0 1
3736.1.e \(\chi_{3736}(933, \cdot)\) 3736.1.e.a 6 1
3736.1.e.b 6
3736.1.f \(\chi_{3736}(2803, \cdot)\) None 0 1
3736.1.g \(\chi_{3736}(2801, \cdot)\) 3736.1.g.a 2 1
3736.1.k \(\chi_{3736}(33, \cdot)\) None 0 232
3736.1.l \(\chi_{3736}(3, \cdot)\) 3736.1.l.a 232 232
3736.1.m \(\chi_{3736}(5, \cdot)\) None 0 232
3736.1.n \(\chi_{3736}(7, \cdot)\) None 0 232

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3736))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3736)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(467))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(934))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1868))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3736))\)\(^{\oplus 1}\)