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Properties

Label 4023.2
Level 4023
Weight 2
Dimension 471206
Nonzero newspaces 18
Sturm bound 2397600

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Defining parameters

Level: \( N \) = \( 4023 = 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 18 \)
Sturm bound: \(2397600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4023))\).

Total New Old
Modular forms 603840 475910 127930
Cusp forms 594961 471206 123755
Eisenstein series 8879 4704 4175

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4023))\)

We only show spaces with even 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
4023.2.a \(\chi_{4023}(1, \cdot)\) 4023.2.a.a 18 1
4023.2.a.b 18
4023.2.a.c 24
4023.2.a.d 24
4023.2.a.e 25
4023.2.a.f 25
4023.2.a.g 32
4023.2.a.h 32
4023.2.c \(\chi_{4023}(595, \cdot)\) n/a 200 1
4023.2.e \(\chi_{4023}(1342, \cdot)\) n/a 296 2
4023.2.f \(\chi_{4023}(701, \cdot)\) n/a 400 2
4023.2.i \(\chi_{4023}(1936, \cdot)\) n/a 296 2
4023.2.k \(\chi_{4023}(448, \cdot)\) n/a 2664 6
4023.2.m \(\chi_{4023}(44, \cdot)\) n/a 592 4
4023.2.p \(\chi_{4023}(148, \cdot)\) n/a 2688 6
4023.2.r \(\chi_{4023}(254, \cdot)\) n/a 5376 12
4023.2.s \(\chi_{4023}(28, \cdot)\) n/a 7200 36
4023.2.u \(\chi_{4023}(82, \cdot)\) n/a 7200 36
4023.2.w \(\chi_{4023}(19, \cdot)\) n/a 10656 72
4023.2.y \(\chi_{4023}(134, \cdot)\) n/a 14400 72
4023.2.ba \(\chi_{4023}(64, \cdot)\) n/a 10656 72
4023.2.bc \(\chi_{4023}(16, \cdot)\) n/a 96768 216
4023.2.bd \(\chi_{4023}(8, \cdot)\) n/a 21312 144
4023.2.bf \(\chi_{4023}(4, \cdot)\) n/a 96768 216
4023.2.bi \(\chi_{4023}(2, \cdot)\) n/a 193536 432

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4023))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4023)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(149))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(447))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1341))\)\(^{\oplus 2}\)