Properties

Label 799.1
Level 799
Weight 1
Dimension 41
Nonzero newspaces 3
Newform subspaces 8
Sturm bound 52992
Trace bound 1

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 799 = 17 \cdot 47 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 3 \)
Newform subspaces: \( 8 \)
Sturm bound: \(52992\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(799))\).

Total New Old
Modular forms 781 715 66
Cusp forms 45 41 4
Eisenstein series 736 674 62

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 41 0 0 0

Trace form

\( 41q - 3q^{4} + q^{9} + O(q^{10}) \) \( 41q - 3q^{4} + q^{9} - 10q^{12} - 10q^{14} - 7q^{16} - 2q^{17} - 10q^{18} - 10q^{24} + q^{25} - 10q^{32} - 3q^{36} - 10q^{42} - 7q^{47} + 30q^{48} + q^{49} - 8q^{50} - 5q^{51} - 4q^{53} + 30q^{54} - 4q^{55} + 30q^{56} - 10q^{63} - 11q^{64} - 11q^{68} - 10q^{72} + q^{81} - 14q^{83} + 70q^{84} - 4q^{89} - 10q^{96} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(799))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
799.1.c \(\chi_{799}(798, \cdot)\) 799.1.c.a 1 1
799.1.c.b 2
799.1.c.c 4
799.1.c.d 4
799.1.d \(\chi_{799}(375, \cdot)\) None 0 1
799.1.e \(\chi_{799}(140, \cdot)\) 799.1.e.a 2 2
799.1.e.b 8
799.1.h \(\chi_{799}(93, \cdot)\) 799.1.h.a 4 4
799.1.h.b 16
799.1.i \(\chi_{799}(48, \cdot)\) None 0 8
799.1.l \(\chi_{799}(35, \cdot)\) None 0 22
799.1.m \(\chi_{799}(33, \cdot)\) None 0 22
799.1.p \(\chi_{799}(13, \cdot)\) None 0 44
799.1.q \(\chi_{799}(15, \cdot)\) None 0 88
799.1.t \(\chi_{799}(3, \cdot)\) None 0 176

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(799))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(799)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(47))\)\(^{\oplus 2}\)