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Properties

Label 751.1
Level 751
Weight 1
Dimension 9
Nonzero newspaces 1
Newform subspaces 4
Sturm bound 47000
Trace bound 0

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Defining parameters

Level: \( N \) = \( 751 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 4 \)
Sturm bound: \(47000\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(751))\).

Total New Old
Modular forms 384 384 0
Cusp forms 9 9 0
Eisenstein series 375 375 0

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 7 0 2 0

Trace form

\( 9 q - 3 q^{2} + 6 q^{4} - q^{5} + 5 q^{9} + O(q^{10}) \) \( 9 q - 3 q^{2} + 6 q^{4} - q^{5} + 5 q^{9} - 2 q^{10} + q^{13} + 3 q^{16} + q^{18} + q^{19} - 3 q^{20} + 4 q^{21} - 3 q^{23} + 4 q^{25} - 4 q^{26} - 3 q^{32} + 4 q^{33} + 6 q^{36} + q^{37} - 4 q^{38} - 4 q^{40} - 4 q^{42} - q^{43} - q^{45} + q^{47} + 5 q^{49} - q^{50} + 4 q^{51} - 3 q^{52} - 3 q^{53} - 3 q^{59} + q^{61} + 6 q^{64} - 2 q^{65} - 4 q^{66} - q^{71} - 4 q^{72} - 4 q^{74} - 3 q^{76} - 4 q^{77} - 5 q^{80} + 5 q^{81} - 2 q^{86} + q^{89} - 2 q^{90} - 3 q^{92} - 4 q^{94} - 2 q^{95} + q^{97} + q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(751))\)

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
751.1.b \(\chi_{751}(750, \cdot)\) 751.1.b.a 1 1
751.1.b.b 2
751.1.b.c 2
751.1.b.d 4
751.1.e \(\chi_{751}(73, \cdot)\) None 0 2
751.1.f \(\chi_{751}(182, \cdot)\) None 0 4
751.1.i \(\chi_{751}(78, \cdot)\) None 0 8
751.1.j \(\chi_{751}(41, \cdot)\) None 0 20
751.1.m \(\chi_{751}(11, \cdot)\) None 0 40
751.1.n \(\chi_{751}(6, \cdot)\) None 0 100
751.1.p \(\chi_{751}(3, \cdot)\) None 0 200