Properties

Label 4004.2.iz
Level $4004$
Weight $2$
Character orbit 4004.iz
Rep. character $\chi_{4004}(85,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $1344$
Sturm bound $1344$

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Defining parameters

Level: \( N \) \(=\) \( 4004 = 2^{2} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4004.iz (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 143 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(1344\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(4004, [\chi])\).

Total New Old
Modular forms 10944 1344 9600
Cusp forms 10560 1344 9216
Eisenstein series 384 0 384

Decomposition of \(S_{2}^{\mathrm{new}}(4004, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(4004, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(4004, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(143, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(286, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(572, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1001, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(2002, [\chi])\)\(^{\oplus 2}\)