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Properties

Label 888.1
Level 888
Weight 1
Dimension 12
Nonzero newspaces 1
Newform subspaces 5
Sturm bound 43776
Trace bound 0

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Defining parameters

Level: \( N \) = \( 888 = 2^{3} \cdot 3 \cdot 37 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 5 \)
Sturm bound: \(43776\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(888))\).

Total New Old
Modular forms 984 152 832
Cusp forms 120 12 108
Eisenstein series 864 140 724

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 12 0 0 0

Trace form

\( 12 q + 4 q^{4} - 4 q^{7} - 4 q^{9} + O(q^{10}) \) \( 12 q + 4 q^{4} - 4 q^{7} - 4 q^{9} + 4 q^{16} - 4 q^{25} - 12 q^{28} - 8 q^{30} - 4 q^{33} + 4 q^{34} + 4 q^{36} + 8 q^{40} - 4 q^{46} + 8 q^{48} + 8 q^{49} + 8 q^{58} - 4 q^{63} + 4 q^{64} - 8 q^{70} - 4 q^{73} - 4 q^{78} + 12 q^{81} - 8 q^{84} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(888))\)

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
888.1.b \(\chi_{888}(295, \cdot)\) None 0 1
888.1.d \(\chi_{888}(667, \cdot)\) None 0 1
888.1.g \(\chi_{888}(593, \cdot)\) None 0 1
888.1.i \(\chi_{888}(221, \cdot)\) 888.1.i.a 1 1
888.1.i.b 1
888.1.i.c 1
888.1.i.d 1
888.1.i.e 8
888.1.k \(\chi_{888}(223, \cdot)\) None 0 1
888.1.m \(\chi_{888}(739, \cdot)\) None 0 1
888.1.n \(\chi_{888}(665, \cdot)\) None 0 1
888.1.p \(\chi_{888}(149, \cdot)\) None 0 1
888.1.s \(\chi_{888}(191, \cdot)\) None 0 2
888.1.u \(\chi_{888}(179, \cdot)\) None 0 2
888.1.v \(\chi_{888}(265, \cdot)\) None 0 2
888.1.x \(\chi_{888}(253, \cdot)\) None 0 2
888.1.ba \(\chi_{888}(233, \cdot)\) None 0 2
888.1.bb \(\chi_{888}(269, \cdot)\) None 0 2
888.1.bc \(\chi_{888}(343, \cdot)\) None 0 2
888.1.be \(\chi_{888}(307, \cdot)\) None 0 2
888.1.bg \(\chi_{888}(137, \cdot)\) None 0 2
888.1.bi \(\chi_{888}(101, \cdot)\) None 0 2
888.1.bl \(\chi_{888}(175, \cdot)\) None 0 2
888.1.bn \(\chi_{888}(211, \cdot)\) None 0 2
888.1.bq \(\chi_{888}(97, \cdot)\) None 0 4
888.1.bs \(\chi_{888}(325, \cdot)\) None 0 4
888.1.bt \(\chi_{888}(23, \cdot)\) None 0 4
888.1.bv \(\chi_{888}(251, \cdot)\) None 0 4
888.1.bx \(\chi_{888}(67, \cdot)\) None 0 6
888.1.bz \(\chi_{888}(77, \cdot)\) None 0 6
888.1.ca \(\chi_{888}(53, \cdot)\) None 0 6
888.1.cd \(\chi_{888}(379, \cdot)\) None 0 6
888.1.ce \(\chi_{888}(41, \cdot)\) None 0 6
888.1.ch \(\chi_{888}(151, \cdot)\) None 0 6
888.1.ci \(\chi_{888}(7, \cdot)\) None 0 6
888.1.cl \(\chi_{888}(305, \cdot)\) None 0 6
888.1.cm \(\chi_{888}(13, \cdot)\) None 0 12
888.1.cn \(\chi_{888}(35, \cdot)\) None 0 12
888.1.cq \(\chi_{888}(143, \cdot)\) None 0 12
888.1.cr \(\chi_{888}(217, \cdot)\) None 0 12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(888))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(888)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(111))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(296))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(444))\)\(^{\oplus 2}\)