Properties

Label 8002.2.v
Level 8002
Weight 2
Character orbit v
Rep. character \(\chi_{8002}(7,\cdot)\)
Character field \(\Q(\zeta_{1000})\)
Dimension 133600
Sturm bound 2001

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Defining parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.v (of order \(1000\) and degree \(400\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 4001 \)
Character field: \(\Q(\zeta_{1000})\)
Sturm bound: \(2001\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(8002, [\chi])\).

Total New Old
Modular forms 400800 133600 267200
Cusp forms 399200 133600 265600
Eisenstein series 1600 0 1600

Decomposition of \(S_{2}^{\mathrm{new}}(8002, [\chi])\) into irreducible Hecke orbits

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(8002, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(8002, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(4001, [\chi])\)\(^{\oplus 2}\)