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Properties

Label 817.1
Level 817
Weight 1
Dimension 20
Nonzero newspaces 3
Newform subspaces 3
Sturm bound 55440
Trace bound 1

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Defining parameters

Level: \( N \) = \( 817 = 19 \cdot 43 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 3 \)
Sturm bound: \(55440\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(817))\).

Total New Old
Modular forms 776 716 60
Cusp forms 20 20 0
Eisenstein series 756 696 60

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

\( 20 q - q^{4} - 2 q^{5} - 2 q^{7} - q^{9} + O(q^{10}) \) \( 20 q - q^{4} - 2 q^{5} - 2 q^{7} - q^{9} - 2 q^{11} - q^{16} - 2 q^{17} - q^{19} - 2 q^{20} - 2 q^{23} - 3 q^{25} - 2 q^{28} - 4 q^{35} - q^{36} + 20 q^{43} - 2 q^{44} + 19 q^{45} - 2 q^{47} - 3 q^{49} - 4 q^{55} - 2 q^{61} - 2 q^{63} - q^{64} - 2 q^{68} - 2 q^{73} - q^{76} - 4 q^{77} - 2 q^{80} - q^{81} - 2 q^{83} - 4 q^{85} - 2 q^{92} - 2 q^{95} - 2 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(817))\)

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
817.1.b \(\chi_{817}(343, \cdot)\) None 0 1
817.1.c \(\chi_{817}(474, \cdot)\) None 0 1
817.1.i \(\chi_{817}(208, \cdot)\) 817.1.i.a 2 2
817.1.j \(\chi_{817}(381, \cdot)\) None 0 2
817.1.n \(\chi_{817}(596, \cdot)\) None 0 2
817.1.o \(\chi_{817}(122, \cdot)\) None 0 2
817.1.p \(\chi_{817}(259, \cdot)\) None 0 2
817.1.q \(\chi_{817}(350, \cdot)\) None 0 2
817.1.r \(\chi_{817}(429, \cdot)\) None 0 2
817.1.s \(\chi_{817}(7, \cdot)\) None 0 2
817.1.z \(\chi_{817}(170, \cdot)\) 817.1.z.a 6 6
817.1.ba \(\chi_{817}(39, \cdot)\) None 0 6
817.1.bc \(\chi_{817}(80, \cdot)\) None 0 6
817.1.bd \(\chi_{817}(135, \cdot)\) None 0 6
817.1.be \(\chi_{817}(173, \cdot)\) None 0 6
817.1.bh \(\chi_{817}(252, \cdot)\) None 0 6
817.1.bi \(\chi_{817}(42, \cdot)\) None 0 6
817.1.bj \(\chi_{817}(79, \cdot)\) None 0 6
817.1.bp \(\chi_{817}(45, \cdot)\) None 0 12
817.1.bq \(\chi_{817}(26, \cdot)\) None 0 12
817.1.br \(\chi_{817}(84, \cdot)\) None 0 12
817.1.bs \(\chi_{817}(160, \cdot)\) None 0 12
817.1.bt \(\chi_{817}(31, \cdot)\) None 0 12
817.1.bu \(\chi_{817}(30, \cdot)\) None 0 12
817.1.by \(\chi_{817}(20, \cdot)\) None 0 12
817.1.bz \(\chi_{817}(56, \cdot)\) 817.1.bz.a 12 12
817.1.cd \(\chi_{817}(63, \cdot)\) None 0 36
817.1.cf \(\chi_{817}(21, \cdot)\) None 0 36
817.1.cg \(\chi_{817}(13, \cdot)\) None 0 36
817.1.ch \(\chi_{817}(82, \cdot)\) None 0 36
817.1.ci \(\chi_{817}(5, \cdot)\) None 0 36
817.1.cl \(\chi_{817}(10, \cdot)\) None 0 36