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Properties

Label 3879.1
Level 3879
Weight 1
Dimension 56
Nonzero newspaces 2
Newform subspaces 6
Sturm bound 1114560
Trace bound 1

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Defining parameters

Level: \( N \) = \( 3879 = 3^{2} \cdot 431 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 6 \)
Sturm bound: \(1114560\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3879))\).

Total New Old
Modular forms 3542 1987 1555
Cusp forms 102 56 46
Eisenstein series 3440 1931 1509

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 52 4 0 0

Trace form

\( 56 q + 3 q^{2} - 4 q^{3} - 12 q^{4} + 3 q^{5} - 2 q^{6} + 6 q^{8} + 4 q^{9} + O(q^{10}) \) \( 56 q + 3 q^{2} - 4 q^{3} - 12 q^{4} + 3 q^{5} - 2 q^{6} + 6 q^{8} + 4 q^{9} + 2 q^{10} + 3 q^{11} - 2 q^{15} - 11 q^{16} + 2 q^{18} - q^{19} + 3 q^{20} - 4 q^{22} - q^{23} - 4 q^{24} - 12 q^{25} - 4 q^{27} + 3 q^{29} - 4 q^{30} + 3 q^{32} - 2 q^{33} + 2 q^{38} - 2 q^{40} + 3 q^{41} + 3 q^{44} + 2 q^{45} - 6 q^{46} - 2 q^{48} - 11 q^{49} + 3 q^{50} + q^{53} - 2 q^{54} + 2 q^{55} - 4 q^{58} + 3 q^{59} - 3 q^{61} + 53 q^{64} + 2 q^{66} + 2 q^{69} + 4 q^{72} - 3 q^{76} + 9 q^{80} + 4 q^{81} + 2 q^{82} - 2 q^{87} - 2 q^{88} + 4 q^{90} - 4 q^{91} + 3 q^{92} + 2 q^{95} - 3 q^{97} + q^{98} + 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3879))\)

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
3879.1.c \(\chi_{3879}(863, \cdot)\) None 0 1
3879.1.d \(\chi_{3879}(3016, \cdot)\) 3879.1.d.a 1 1
3879.1.d.b 3
3879.1.d.c 6
3879.1.g \(\chi_{3879}(430, \cdot)\) 3879.1.g.a 4 2
3879.1.g.b 6
3879.1.g.c 36
3879.1.h \(\chi_{3879}(2156, \cdot)\) None 0 2
3879.1.j \(\chi_{3879}(116, \cdot)\) None 0 4
3879.1.l \(\chi_{3879}(1198, \cdot)\) None 0 4
3879.1.n \(\chi_{3879}(457, \cdot)\) None 0 8
3879.1.p \(\chi_{3879}(95, \cdot)\) None 0 8
3879.1.r \(\chi_{3879}(415, \cdot)\) None 0 42
3879.1.s \(\chi_{3879}(8, \cdot)\) None 0 42
3879.1.x \(\chi_{3879}(2, \cdot)\) None 0 84
3879.1.y \(\chi_{3879}(94, \cdot)\) None 0 84
3879.1.z \(\chi_{3879}(28, \cdot)\) None 0 168
3879.1.bb \(\chi_{3879}(44, \cdot)\) None 0 168
3879.1.bd \(\chi_{3879}(5, \cdot)\) None 0 336
3879.1.bf \(\chi_{3879}(7, \cdot)\) None 0 336

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3879))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3879)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(431))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1293))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3879))\)\(^{\oplus 1}\)