Properties

Label 8012.2
Level 8012
Weight 2
Dimension 1168167
Nonzero newspaces 16
Sturm bound 8024016

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Defining parameters

Level: \( N \) = \( 8012 = 2^{2} \cdot 2003 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 16 \)
Sturm bound: \(8024016\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8012))\).

Total New Old
Modular forms 2011009 1172171 838838
Cusp forms 2001000 1168167 832833
Eisenstein series 10009 4004 6005

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8012))\)

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
8012.2.a \(\chi_{8012}(1, \cdot)\) 8012.2.a.a 79 1
8012.2.a.b 88
8012.2.b \(\chi_{8012}(8011, \cdot)\) n/a 1000 1
8012.2.e \(\chi_{8012}(485, \cdot)\) n/a 1002 6
8012.2.f \(\chi_{8012}(685, \cdot)\) n/a 1670 10
8012.2.g \(\chi_{8012}(89, \cdot)\) n/a 2004 12
8012.2.j \(\chi_{8012}(5035, \cdot)\) n/a 6000 6
8012.2.m \(\chi_{8012}(1243, \cdot)\) n/a 10000 10
8012.2.p \(\chi_{8012}(87, \cdot)\) n/a 12000 12
8012.2.q \(\chi_{8012}(57, \cdot)\) n/a 10020 60
8012.2.r \(\chi_{8012}(53, \cdot)\) n/a 12024 72
8012.2.s \(\chi_{8012}(113, \cdot)\) n/a 20040 120
8012.2.t \(\chi_{8012}(99, \cdot)\) n/a 60000 60
8012.2.w \(\chi_{8012}(295, \cdot)\) n/a 72000 72
8012.2.z \(\chi_{8012}(11, \cdot)\) n/a 120000 120
8012.2.bc \(\chi_{8012}(9, \cdot)\) n/a 120240 720
8012.2.bf \(\chi_{8012}(7, \cdot)\) n/a 720000 720

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8012))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8012)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(2003))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4006))\)\(^{\oplus 2}\)