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Properties

Label 779.1
Level 779
Weight 1
Dimension 12
Nonzero newspaces 2
Newform subspaces 3
Sturm bound 50400
Trace bound 1

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Defining parameters

Level: \( N \) = \( 779 = 19 \cdot 41 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 3 \)
Sturm bound: \(50400\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(779))\).

Total New Old
Modular forms 732 674 58
Cusp forms 12 12 0
Eisenstein series 720 662 58

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 4 0 0 8

Trace form

\( 12 q + 10 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} + 2 q^{9} + O(q^{10}) \) \( 12 q + 10 q^{4} - 4 q^{5} - 4 q^{6} - 2 q^{7} + 2 q^{9} + 4 q^{16} + 6 q^{17} + 2 q^{19} - 6 q^{20} - 6 q^{23} - 2 q^{24} + 2 q^{25} - 8 q^{26} - 4 q^{28} + 6 q^{30} - 2 q^{35} + 2 q^{36} - 4 q^{42} - 2 q^{43} - 6 q^{45} - 6 q^{47} + 4 q^{49} - 4 q^{54} - 2 q^{57} - 6 q^{58} - 6 q^{61} + 8 q^{64} + 12 q^{68} - 10 q^{73} + 8 q^{74} + 4 q^{76} - 2 q^{80} - 8 q^{81} + 4 q^{82} + 6 q^{83} - 4 q^{85} - 6 q^{87} - 10 q^{92} + 2 q^{95} + 8 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(779))\)

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
779.1.b \(\chi_{779}(493, \cdot)\) None 0 1
779.1.c \(\chi_{779}(778, \cdot)\) 779.1.c.a 2 1
779.1.c.b 2
779.1.g \(\chi_{779}(132, \cdot)\) None 0 2
779.1.j \(\chi_{779}(122, \cdot)\) None 0 2
779.1.k \(\chi_{779}(411, \cdot)\) None 0 2
779.1.m \(\chi_{779}(96, \cdot)\) None 0 4
779.1.p \(\chi_{779}(18, \cdot)\) 779.1.p.a 8 4
779.1.q \(\chi_{779}(113, \cdot)\) None 0 4
779.1.r \(\chi_{779}(50, \cdot)\) None 0 4
779.1.u \(\chi_{779}(124, \cdot)\) None 0 6
779.1.w \(\chi_{779}(40, \cdot)\) None 0 6
779.1.x \(\chi_{779}(512, \cdot)\) None 0 8
779.1.z \(\chi_{779}(68, \cdot)\) None 0 8
779.1.bb \(\chi_{779}(31, \cdot)\) None 0 8
779.1.bc \(\chi_{779}(141, \cdot)\) None 0 8
779.1.be \(\chi_{779}(32, \cdot)\) None 0 12
779.1.bg \(\chi_{779}(58, \cdot)\) None 0 16
779.1.bk \(\chi_{779}(8, \cdot)\) None 0 16
779.1.bm \(\chi_{779}(44, \cdot)\) None 0 24
779.1.bn \(\chi_{779}(72, \cdot)\) None 0 24
779.1.bp \(\chi_{779}(10, \cdot)\) None 0 24
779.1.br \(\chi_{779}(7, \cdot)\) None 0 32
779.1.bt \(\chi_{779}(2, \cdot)\) None 0 48
779.1.bu \(\chi_{779}(6, \cdot)\) None 0 96