Properties

Label 4021.2
Level 4021
Weight 2
Dimension 671676
Nonzero newspaces 16
Sturm bound 2694740

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Defining parameters

Level: \( N \) = \( 4021 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(2694740\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4021))\).

Total New Old
Modular forms 675695 675695 0
Cusp forms 671676 671676 0
Eisenstein series 4019 4019 0

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4021))\)

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
4021.2.a \(\chi_{4021}(1, \cdot)\) 4021.2.a.a 1 1
4021.2.a.b 151
4021.2.a.c 182
4021.2.b \(\chi_{4021}(4020, \cdot)\) n/a 334 1
4021.2.c \(\chi_{4021}(1812, \cdot)\) n/a 668 2
4021.2.e \(\chi_{4021}(2401, \cdot)\) n/a 1332 4
4021.2.f \(\chi_{4021}(1813, \cdot)\) n/a 670 2
4021.2.g \(\chi_{4021}(49, \cdot)\) n/a 1336 4
4021.2.i \(\chi_{4021}(37, \cdot)\) n/a 2672 8
4021.2.k \(\chi_{4021}(110, \cdot)\) n/a 2680 8
4021.2.m \(\chi_{4021}(67, \cdot)\) n/a 21978 66
4021.2.n \(\chi_{4021}(13, \cdot)\) n/a 22044 66
4021.2.o \(\chi_{4021}(77, \cdot)\) n/a 44088 132
4021.2.q \(\chi_{4021}(27, \cdot)\) n/a 87912 264
4021.2.r \(\chi_{4021}(53, \cdot)\) n/a 44220 132
4021.2.s \(\chi_{4021}(17, \cdot)\) n/a 88176 264
4021.2.u \(\chi_{4021}(3, \cdot)\) n/a 176352 528
4021.2.w \(\chi_{4021}(4, \cdot)\) n/a 176880 528

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