Properties

Label 4012.2.t
Level $4012$
Weight $2$
Character orbit 4012.t
Rep. character $\chi_{4012}(589,\cdot)$
Character field $\Q(\zeta_{16})$
Dimension $720$
Sturm bound $1080$

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Defining parameters

Level: \( N \) \(=\) \( 4012 = 2^{2} \cdot 17 \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4012.t (of order \(16\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1003 \)
Character field: \(\Q(\zeta_{16})\)
Sturm bound: \(1080\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4012, [\chi])\).

Total New Old
Modular forms 4368 720 3648
Cusp forms 4272 720 3552
Eisenstein series 96 0 96

Decomposition of \(S_{2}^{\mathrm{new}}(4012, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(4012, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4012, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(1003, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2006, [\chi])\)\(^{\oplus 2}\)