↑

Properties

Label 876.1
Level 876
Weight 1
Dimension 28
Nonzero newspaces 4
Newform subspaces 6
Sturm bound 42624
Trace bound 3

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 876 = 2^{2} \cdot 3 \cdot 73 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 6 \)
Sturm bound: \(42624\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(876))\).

Total New Old
Modular forms 827 172 655
Cusp forms 107 28 79
Eisenstein series 720 144 576

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 28 0 0 0

Trace form

\( 28 q + 4 q^{9} + O(q^{10}) \) \( 28 q + 4 q^{9} + 4 q^{25} + 4 q^{49} - 4 q^{55} - 16 q^{57} - 4 q^{61} - 16 q^{67} - 4 q^{75} - 8 q^{81} - 4 q^{85} - 12 q^{91} - 4 q^{97} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(876))\)

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
876.1.d \(\chi_{876}(293, \cdot)\) None 0 1
876.1.e \(\chi_{876}(583, \cdot)\) None 0 1
876.1.f \(\chi_{876}(439, \cdot)\) None 0 1
876.1.g \(\chi_{876}(437, \cdot)\) 876.1.g.a 1 1
876.1.g.b 1
876.1.g.c 2
876.1.k \(\chi_{876}(173, \cdot)\) None 0 2
876.1.m \(\chi_{876}(319, \cdot)\) None 0 2
876.1.n \(\chi_{876}(65, \cdot)\) None 0 2
876.1.o \(\chi_{876}(283, \cdot)\) None 0 2
876.1.s \(\chi_{876}(211, \cdot)\) None 0 2
876.1.t \(\chi_{876}(137, \cdot)\) None 0 2
876.1.v \(\chi_{876}(229, \cdot)\) None 0 4
876.1.w \(\chi_{876}(83, \cdot)\) None 0 4
876.1.z \(\chi_{876}(295, \cdot)\) None 0 4
876.1.bb \(\chi_{876}(149, \cdot)\) None 0 4
876.1.be \(\chi_{876}(91, \cdot)\) None 0 6
876.1.bf \(\chi_{876}(77, \cdot)\) 876.1.bf.a 6 6
876.1.bg \(\chi_{876}(55, \cdot)\) None 0 6
876.1.bh \(\chi_{876}(41, \cdot)\) 876.1.bh.a 6 6
876.1.bl \(\chi_{876}(167, \cdot)\) None 0 8
876.1.bm \(\chi_{876}(313, \cdot)\) None 0 8
876.1.bp \(\chi_{876}(19, \cdot)\) None 0 12
876.1.br \(\chi_{876}(257, \cdot)\) 876.1.br.a 12 12
876.1.bt \(\chi_{876}(11, \cdot)\) None 0 24
876.1.bv \(\chi_{876}(13, \cdot)\) None 0 24

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(876))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(876)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(219))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(292))\)\(^{\oplus 2}\)