Properties

Label 2183.1
Level 2183
Weight 1
Dimension 24
Nonzero newspaces 1
Newform subspaces 8
Sturm bound 396720
Trace bound 0

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Defining parameters

Level: \( N \) = \( 2183 = 37 \cdot 59 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 8 \)
Sturm bound: \(396720\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2183))\).

Total New Old
Modular forms 2114 2018 96
Cusp forms 26 24 2
Eisenstein series 2088 1994 94

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 4 0

Trace form

\( 24 q - 2 q^{3} + 18 q^{4} - 6 q^{7} + 14 q^{9} + O(q^{10}) \) \( 24 q - 2 q^{3} + 18 q^{4} - 6 q^{7} + 14 q^{9} - 6 q^{12} + 12 q^{16} - 4 q^{21} + 16 q^{25} - 8 q^{26} - 4 q^{27} - 6 q^{28} + 12 q^{36} - 6 q^{41} - 4 q^{46} - 10 q^{48} + 18 q^{49} - 6 q^{53} - 8 q^{62} - 2 q^{63} + 18 q^{64} - 6 q^{71} + 2 q^{74} - 2 q^{75} - 8 q^{78} + 20 q^{81} - 12 q^{84} - 8 q^{85} - 4 q^{86} + 8 q^{95} + O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2183))\)

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
2183.1.c \(\chi_{2183}(1592, \cdot)\) None 0 1
2183.1.d \(\chi_{2183}(2182, \cdot)\) 2183.1.d.a 1 1
2183.1.d.b 1
2183.1.d.c 2
2183.1.d.d 2
2183.1.d.e 3
2183.1.d.f 3
2183.1.d.g 6
2183.1.d.h 6
2183.1.g \(\chi_{2183}(709, \cdot)\) None 0 2
2183.1.h \(\chi_{2183}(471, \cdot)\) None 0 2
2183.1.i \(\chi_{2183}(766, \cdot)\) None 0 2
2183.1.m \(\chi_{2183}(60, \cdot)\) None 0 4
2183.1.o \(\chi_{2183}(530, \cdot)\) None 0 6
2183.1.p \(\chi_{2183}(58, \cdot)\) None 0 6
2183.1.r \(\chi_{2183}(237, \cdot)\) None 0 12
2183.1.t \(\chi_{2183}(73, \cdot)\) None 0 28
2183.1.u \(\chi_{2183}(38, \cdot)\) None 0 28
2183.1.x \(\chi_{2183}(68, \cdot)\) None 0 56
2183.1.ba \(\chi_{2183}(10, \cdot)\) None 0 56
2183.1.bb \(\chi_{2183}(11, \cdot)\) None 0 56
2183.1.bd \(\chi_{2183}(29, \cdot)\) None 0 112
2183.1.bf \(\chi_{2183}(30, \cdot)\) None 0 168
2183.1.bg \(\chi_{2183}(33, \cdot)\) None 0 168
2183.1.bj \(\chi_{2183}(5, \cdot)\) None 0 336

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2183))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2183)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 2}\)