Properties

Label 8035.2
Level 8035
Weight 2
Dimension 2362425
Nonzero newspaces 12
Sturm bound 10329792

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Defining parameters

Level: \( N \) = \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 12 \)
Sturm bound: \(10329792\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8035))\).

Total New Old
Modular forms 2588872 2372057 216815
Cusp forms 2576025 2362425 213600
Eisenstein series 12847 9632 3215

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8035))\)

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
8035.2.a \(\chi_{8035}(1, \cdot)\) 8035.2.a.a 1 1
8035.2.a.b 114
8035.2.a.c 127
8035.2.a.d 140
8035.2.a.e 153
8035.2.b \(\chi_{8035}(6429, \cdot)\) n/a 802 1
8035.2.e \(\chi_{8035}(3213, \cdot)\) n/a 1604 2
8035.2.g \(\chi_{8035}(1046, \cdot)\) n/a 5360 10
8035.2.j \(\chi_{8035}(444, \cdot)\) n/a 8020 10
8035.2.l \(\chi_{8035}(1163, \cdot)\) n/a 16040 20
8035.2.m \(\chi_{8035}(96, \cdot)\) n/a 38592 72
8035.2.p \(\chi_{8035}(34, \cdot)\) n/a 57744 72
8035.2.r \(\chi_{8035}(38, \cdot)\) n/a 115488 144
8035.2.s \(\chi_{8035}(6, \cdot)\) n/a 385920 720
8035.2.t \(\chi_{8035}(4, \cdot)\) n/a 577440 720
8035.2.w \(\chi_{8035}(7, \cdot)\) n/a 1154880 1440

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8035))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8035)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1607))\)\(^{\oplus 2}\)