Properties

Label 869.1
Level 869
Weight 1
Dimension 20
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 62400
Trace bound 0

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Defining parameters

Level: \( N \) = \( 869 = 11 \cdot 79 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(62400\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(869))\).

Total New Old
Modular forms 804 712 92
Cusp forms 24 20 4
Eisenstein series 780 692 88

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 0 0

Trace form

\( 20q - 5q^{4} - 5q^{9} + O(q^{10}) \) \( 20q - 5q^{4} - 5q^{9} - 5q^{16} + 15q^{20} - 5q^{22} - 5q^{25} + 15q^{26} - 10q^{32} - 5q^{36} - 10q^{40} - 5q^{49} - 10q^{50} - 10q^{62} - 5q^{64} - 10q^{76} - 5q^{79} - 10q^{80} - 5q^{81} + 15q^{83} - 5q^{88} + 15q^{92} + 15q^{95} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(869))\)

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
869.1.c \(\chi_{869}(791, \cdot)\) None 0 1
869.1.d \(\chi_{869}(78, \cdot)\) None 0 1
869.1.g \(\chi_{869}(56, \cdot)\) None 0 2
869.1.h \(\chi_{869}(450, \cdot)\) None 0 2
869.1.j \(\chi_{869}(157, \cdot)\) 869.1.j.a 20 4
869.1.k \(\chi_{869}(238, \cdot)\) None 0 4
869.1.o \(\chi_{869}(12, \cdot)\) None 0 12
869.1.p \(\chi_{869}(10, \cdot)\) None 0 12
869.1.s \(\chi_{869}(134, \cdot)\) None 0 8
869.1.t \(\chi_{869}(103, \cdot)\) None 0 8
869.1.x \(\chi_{869}(32, \cdot)\) None 0 24
869.1.y \(\chi_{869}(34, \cdot)\) None 0 24
869.1.ba \(\chi_{869}(8, \cdot)\) None 0 48
869.1.bb \(\chi_{869}(14, \cdot)\) None 0 48
869.1.bd \(\chi_{869}(3, \cdot)\) None 0 96
869.1.be \(\chi_{869}(2, \cdot)\) None 0 96

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(869))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(869)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(79))\)\(^{\oplus 2}\)