Properties

Label 639.1
Level 639
Weight 1
Dimension 17
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 30240
Trace bound 1

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Defining parameters

Level: \( N \) = \( 639 = 3^{2} \cdot 71 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(30240\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(639))\).

Total New Old
Modular forms 586 328 258
Cusp forms 26 17 9
Eisenstein series 560 311 249

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 17 0 0 0

Trace form

\( 17 q + q^{2} - 5 q^{4} + q^{5} + 2 q^{8} + O(q^{10}) \) \( 17 q + q^{2} - 5 q^{4} + q^{5} + 2 q^{8} - 2 q^{10} - 6 q^{16} + 14 q^{18} - q^{19} + 3 q^{20} - 7 q^{24} - 5 q^{25} + q^{29} - 7 q^{30} + 3 q^{32} - q^{37} - 19 q^{38} - 4 q^{40} - q^{43} - 7 q^{48} - 4 q^{49} + 3 q^{50} - 2 q^{58} - 7 q^{60} + 14 q^{64} + 11 q^{71} - 7 q^{72} - q^{73} + 2 q^{74} + 14 q^{75} - 3 q^{76} - q^{79} - 16 q^{80} + q^{83} + 2 q^{86} - 7 q^{87} + q^{89} + 14 q^{90} + 2 q^{95} - 7 q^{96} + q^{98} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(639))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
639.1.c \(\chi_{639}(143, \cdot)\) None 0 1
639.1.d \(\chi_{639}(496, \cdot)\) 639.1.d.a 3 1
639.1.g \(\chi_{639}(70, \cdot)\) 639.1.g.a 2 2
639.1.g.b 12
639.1.h \(\chi_{639}(356, \cdot)\) None 0 2
639.1.k \(\chi_{639}(46, \cdot)\) None 0 4
639.1.l \(\chi_{639}(125, \cdot)\) None 0 4
639.1.n \(\chi_{639}(181, \cdot)\) None 0 6
639.1.o \(\chi_{639}(116, \cdot)\) None 0 6
639.1.t \(\chi_{639}(5, \cdot)\) None 0 8
639.1.u \(\chi_{639}(85, \cdot)\) None 0 8
639.1.x \(\chi_{639}(20, \cdot)\) None 0 12
639.1.y \(\chi_{639}(34, \cdot)\) None 0 12
639.1.ba \(\chi_{639}(8, \cdot)\) None 0 24
639.1.bb \(\chi_{639}(28, \cdot)\) None 0 24
639.1.bd \(\chi_{639}(7, \cdot)\) None 0 48
639.1.be \(\chi_{639}(2, \cdot)\) None 0 48

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(639))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(639)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(71))\)\(^{\oplus 3}\)