Properties

Label 8044.2
Level 8044
Weight 2
Dimension 1177525
Nonzero newspaces 16
Sturm bound 8088240

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Defining parameters

Level: \( N \) = \( 8044 = 2^{2} \cdot 2011 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(8088240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8044))\).

Total New Old
Modular forms 2027085 1181545 845540
Cusp forms 2017036 1177525 839511
Eisenstein series 10049 4020 6029

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8044))\)

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
8044.2.a \(\chi_{8044}(1, \cdot)\) 8044.2.a.a 80 1
8044.2.a.b 87
8044.2.d \(\chi_{8044}(8043, \cdot)\) n/a 1004 1
8044.2.e \(\chi_{8044}(205, \cdot)\) n/a 336 2
8044.2.f \(\chi_{8044}(2809, \cdot)\) n/a 668 4
8044.2.g \(\chi_{8044}(6239, \cdot)\) n/a 2008 2
8044.2.j \(\chi_{8044}(63, \cdot)\) n/a 4016 4
8044.2.m \(\chi_{8044}(1201, \cdot)\) n/a 1344 8
8044.2.p \(\chi_{8044}(1099, \cdot)\) n/a 8032 8
8044.2.q \(\chi_{8044}(133, \cdot)\) n/a 11022 66
8044.2.r \(\chi_{8044}(147, \cdot)\) n/a 66264 66
8044.2.u \(\chi_{8044}(117, \cdot)\) n/a 22176 132
8044.2.v \(\chi_{8044}(13, \cdot)\) n/a 44088 264
8044.2.y \(\chi_{8044}(15, \cdot)\) n/a 132528 132
8044.2.bb \(\chi_{8044}(27, \cdot)\) n/a 265056 264
8044.2.bc \(\chi_{8044}(5, \cdot)\) n/a 88704 528
8044.2.bd \(\chi_{8044}(3, \cdot)\) n/a 530112 528

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8044))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8044)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(2011))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4022))\)\(^{\oplus 2}\)