Properties

Label 8042.2
Level 8042
Weight 2
Dimension 673684
Nonzero newspaces 16
Sturm bound 8084220

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Defining parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(8084220\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8042))\).

Total New Old
Modular forms 2025075 673684 1351391
Cusp forms 2017036 673684 1343352
Eisenstein series 8039 0 8039

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8042))\)

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
8042.2.a \(\chi_{8042}(1, \cdot)\) 8042.2.a.a 67 1
8042.2.a.b 82
8042.2.a.c 86
8042.2.a.d 101
8042.2.b \(\chi_{8042}(8041, \cdot)\) n/a 336 1
8042.2.c \(\chi_{8042}(5833, \cdot)\) n/a 670 2
8042.2.e \(\chi_{8042}(2401, \cdot)\) n/a 1348 4
8042.2.f \(\chi_{8042}(1813, \cdot)\) n/a 668 2
8042.2.g \(\chi_{8042}(49, \cdot)\) n/a 1344 4
8042.2.i \(\chi_{8042}(37, \cdot)\) n/a 2680 8
8042.2.k \(\chi_{8042}(329, \cdot)\) n/a 2672 8
8042.2.m \(\chi_{8042}(67, \cdot)\) n/a 22242 66
8042.2.n \(\chi_{8042}(13, \cdot)\) n/a 22176 66
8042.2.o \(\chi_{8042}(77, \cdot)\) n/a 44220 132
8042.2.q \(\chi_{8042}(27, \cdot)\) n/a 88968 264
8042.2.r \(\chi_{8042}(53, \cdot)\) n/a 44088 132
8042.2.s \(\chi_{8042}(17, \cdot)\) n/a 88704 264
8042.2.u \(\chi_{8042}(3, \cdot)\) n/a 176880 528
8042.2.w \(\chi_{8042}(39, \cdot)\) n/a 176352 528

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8042))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8042)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(4021))\)\(^{\oplus 2}\)