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Properties

Label 2023.1
Level 2023
Weight 1
Dimension 92
Nonzero newspaces 4
Newform subspaces 13
Sturm bound 332928
Trace bound 1

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Defining parameters

Level: \( N \) = \( 2023 = 7 \cdot 17^{2} \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 4 \)
Newform subspaces: \( 13 \)
Sturm bound: \(332928\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(2023))\).

Total New Old
Modular forms 2500 1935 565
Cusp forms 100 92 8
Eisenstein series 2400 1843 557

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 92 0 0 0

Trace form

\( 92 q + 2 q^{2} - 2 q^{4} + 4 q^{8} - 2 q^{9} + O(q^{10}) \) \( 92 q + 2 q^{2} - 2 q^{4} + 4 q^{8} - 2 q^{9} + 4 q^{15} - 58 q^{18} + 2 q^{21} - 2 q^{25} - 2 q^{30} - 4 q^{32} - 14 q^{35} - 6 q^{36} - 6 q^{42} + 2 q^{43} - 4 q^{49} - 4 q^{50} + 2 q^{53} + 2 q^{60} + 2 q^{64} + 2 q^{67} + 4 q^{70} + 2 q^{72} + 6 q^{84} + 10 q^{86} + 4 q^{93} + 2 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(2023))\)

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
2023.1.c \(\chi_{2023}(1735, \cdot)\) 2023.1.c.a 1 1
2023.1.c.b 1
2023.1.c.c 3
2023.1.c.d 3
2023.1.c.e 4
2023.1.d \(\chi_{2023}(2022, \cdot)\) 2023.1.d.a 2 1
2023.1.d.b 6
2023.1.f \(\chi_{2023}(251, \cdot)\) 2023.1.f.a 4 2
2023.1.f.b 8
2023.1.f.c 12
2023.1.h \(\chi_{2023}(577, \cdot)\) None 0 2
2023.1.i \(\chi_{2023}(290, \cdot)\) None 0 2
2023.1.l \(\chi_{2023}(468, \cdot)\) 2023.1.l.a 8 4
2023.1.l.b 16
2023.1.l.c 24
2023.1.m \(\chi_{2023}(38, \cdot)\) None 0 4
2023.1.o \(\chi_{2023}(736, \cdot)\) None 0 8
2023.1.s \(\chi_{2023}(110, \cdot)\) None 0 8
2023.1.t \(\chi_{2023}(118, \cdot)\) None 0 16
2023.1.u \(\chi_{2023}(69, \cdot)\) None 0 16
2023.1.x \(\chi_{2023}(65, \cdot)\) None 0 16
2023.1.ba \(\chi_{2023}(13, \cdot)\) None 0 32
2023.1.bc \(\chi_{2023}(52, \cdot)\) None 0 32
2023.1.bd \(\chi_{2023}(33, \cdot)\) None 0 32
2023.1.be \(\chi_{2023}(76, \cdot)\) None 0 64
2023.1.bh \(\chi_{2023}(47, \cdot)\) None 0 64
2023.1.bj \(\chi_{2023}(22, \cdot)\) None 0 128
2023.1.bk \(\chi_{2023}(19, \cdot)\) None 0 128
2023.1.bm \(\chi_{2023}(11, \cdot)\) None 0 256

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(2023))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(2023)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 2}\)