Properties

Label 1805.1
Level 1805
Weight 1
Dimension 42
Nonzero newspaces 5
Newform subspaces 7
Sturm bound 259920
Trace bound 1

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Defining parameters

Level: \( N \) = \( 1805 = 5 \cdot 19^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 7 \)
Sturm bound: \(259920\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1805))\).

Total New Old
Modular forms 2064 1448 616
Cusp forms 48 42 6
Eisenstein series 2016 1406 610

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 42 0 0 0

Trace form

\( 42 q - q^{4} + q^{5} + 4 q^{6} - q^{9} + O(q^{10}) \) \( 42 q - q^{4} + q^{5} + 4 q^{6} - q^{9} + 2 q^{11} + q^{16} - 24 q^{20} - 3 q^{25} - 4 q^{26} - 4 q^{30} - 3 q^{36} - 32 q^{39} - 2 q^{44} + 3 q^{45} - 3 q^{49} + 2 q^{55} + 2 q^{61} + 3 q^{64} + 4 q^{74} - 3 q^{80} + q^{81} + 32 q^{96} - 2 q^{99} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1805))\)

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
1805.1.c \(\chi_{1805}(721, \cdot)\) None 0 1
1805.1.d \(\chi_{1805}(1804, \cdot)\) None 0 1
1805.1.f \(\chi_{1805}(362, \cdot)\) 1805.1.f.a 2 2
1805.1.h \(\chi_{1805}(69, \cdot)\) 1805.1.h.a 2 2
1805.1.h.b 4
1805.1.j \(\chi_{1805}(791, \cdot)\) None 0 2
1805.1.m \(\chi_{1805}(68, \cdot)\) 1805.1.m.a 4 4
1805.1.n \(\chi_{1805}(116, \cdot)\) None 0 6
1805.1.o \(\chi_{1805}(299, \cdot)\) 1805.1.o.a 6 6
1805.1.o.b 12
1805.1.r \(\chi_{1805}(28, \cdot)\) 1805.1.r.a 12 12
1805.1.t \(\chi_{1805}(94, \cdot)\) None 0 18
1805.1.u \(\chi_{1805}(56, \cdot)\) None 0 18
1805.1.y \(\chi_{1805}(58, \cdot)\) None 0 36
1805.1.z \(\chi_{1805}(31, \cdot)\) None 0 36
1805.1.bb \(\chi_{1805}(84, \cdot)\) None 0 36
1805.1.bd \(\chi_{1805}(7, \cdot)\) None 0 72
1805.1.bg \(\chi_{1805}(14, \cdot)\) None 0 108
1805.1.bh \(\chi_{1805}(21, \cdot)\) None 0 108
1805.1.bj \(\chi_{1805}(17, \cdot)\) None 0 216

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1805))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1805)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 2}\)