Properties

Label 4022.2
Level 4022
Weight 2
Dimension 168504
Nonzero newspaces 8
Sturm bound 2022060

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Defining parameters

Level: \( N \) = \( 4022 = 2 \cdot 2011 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(2022060\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4022))\).

Total New Old
Modular forms 507525 168504 339021
Cusp forms 503506 168504 335002
Eisenstein series 4019 0 4019

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4022))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
4022.2.a \(\chi_{4022}(1, \cdot)\) 4022.2.a.a 1 1
4022.2.a.b 3
4022.2.a.c 31
4022.2.a.d 37
4022.2.a.e 46
4022.2.a.f 50
4022.2.c \(\chi_{4022}(205, \cdot)\) n/a 334 2
4022.2.d \(\chi_{4022}(2809, \cdot)\) n/a 676 4
4022.2.g \(\chi_{4022}(699, \cdot)\) n/a 1336 8
4022.2.i \(\chi_{4022}(103, \cdot)\) n/a 11154 66
4022.2.k \(\chi_{4022}(115, \cdot)\) n/a 22044 132
4022.2.l \(\chi_{4022}(13, \cdot)\) n/a 44616 264
4022.2.o \(\chi_{4022}(5, \cdot)\) n/a 88176 528

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4022))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4022)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(2011))\)\(^{\oplus 2}\)