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Properties

Label 2004.2.j
Level $2004$
Weight $2$
Character orbit 2004.j
Rep. character $\chi_{2004}(5,\cdot)$
Character field $\Q(\zeta_{166})$
Dimension $4592$
Sturm bound $672$

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Defining parameters

Level: \( N \) \(=\) \( 2004 = 2^{2} \cdot 3 \cdot 167 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2004.j (of order \(166\) and degree \(82\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 501 \)
Character field: \(\Q(\zeta_{166})\)
Sturm bound: \(672\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(2004, [\chi])\).

Total New Old
Modular forms 28044 4592 23452
Cusp forms 27060 4592 22468
Eisenstein series 984 0 984

Trace form

\( 4592 q + 8 q^{9} + O(q^{10}) \) \( 4592 q + 8 q^{9} + 4 q^{19} - 4 q^{21} - 52 q^{25} - 12 q^{27} - 4 q^{31} + 8 q^{33} - 32 q^{49} - 24 q^{57} - 28 q^{61} + 26 q^{63} + 54 q^{75} + 24 q^{81} - 8 q^{85} - 14 q^{87} + 20 q^{93} - 36 q^{97} - 32 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(2004, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(2004, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(2004, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(501, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1002, [\chi])\)\(^{\oplus 2}\)