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Properties

Label 772.1
Level 772
Weight 1
Dimension 47
Nonzero newspaces 9
Newform subspaces 9
Sturm bound 37248
Trace bound 9

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Defining parameters

Level: \( N \) = \( 772 = 2^{2} \cdot 193 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 9 \)
Sturm bound: \(37248\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(772))\).

Total New Old
Modular forms 527 237 290
Cusp forms 47 47 0
Eisenstein series 480 190 290

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 47 0 0 0

Trace form

\( 47 q - q^{2} - q^{4} - 2 q^{5} - q^{8} - q^{9} + O(q^{10}) \) \( 47 q - q^{2} - q^{4} - 2 q^{5} - q^{8} - q^{9} - 2 q^{10} - 2 q^{13} - q^{16} - 2 q^{17} - q^{18} - 2 q^{20} - 3 q^{25} - 2 q^{26} - 2 q^{29} - q^{32} - 2 q^{34} - q^{36} - 2 q^{37} - 2 q^{40} - 2 q^{41} - 2 q^{45} - q^{49} - 3 q^{50} - 2 q^{52} - 2 q^{53} - 2 q^{58} - 2 q^{61} - q^{64} - 4 q^{65} - 2 q^{68} - q^{72} - 2 q^{73} - 2 q^{74} - 2 q^{80} - q^{81} - 2 q^{82} - 4 q^{85} - 2 q^{89} - 2 q^{90} - 2 q^{97} - q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(772))\)

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
772.1.b \(\chi_{772}(771, \cdot)\) 772.1.b.a 1 1
772.1.c \(\chi_{772}(387, \cdot)\) None 0 1
772.1.f \(\chi_{772}(467, \cdot)\) 772.1.f.a 2 2
772.1.h \(\chi_{772}(663, \cdot)\) 772.1.h.a 2 2
772.1.i \(\chi_{772}(471, \cdot)\) 772.1.i.a 2 2
772.1.l \(\chi_{772}(43, \cdot)\) 772.1.l.a 4 4
772.1.m \(\chi_{772}(63, \cdot)\) 772.1.m.a 4 4
772.1.p \(\chi_{772}(3, \cdot)\) 772.1.p.a 8 8
772.1.r \(\chi_{772}(7, \cdot)\) 772.1.r.a 8 8
772.1.t \(\chi_{772}(23, \cdot)\) None 0 16
772.1.u \(\chi_{772}(59, \cdot)\) 772.1.u.a 16 16
772.1.x \(\chi_{772}(13, \cdot)\) None 0 32
772.1.y \(\chi_{772}(31, \cdot)\) None 0 32
772.1.bb \(\chi_{772}(5, \cdot)\) None 0 64