Properties

Label 2004.2.i
Level $2004$
Weight $2$
Character orbit 2004.i
Rep. character $\chi_{2004}(25,\cdot)$
Character field $\Q(\zeta_{83})$
Dimension $2296$
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.i (of order \(83\) and degree \(82\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 167 \)
Character field: \(\Q(\zeta_{83})\)
Sturm bound: \(672\)

Dimensions

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

Total New Old
Modular forms 28044 2296 25748
Cusp forms 27060 2296 24764
Eisenstein series 984 0 984

Trace form

\( 2296q - 28q^{9} + O(q^{10}) \) \( 2296q - 28q^{9} + 4q^{11} - 4q^{13} - 4q^{15} - 16q^{23} - 40q^{25} - 4q^{29} - 8q^{33} + 4q^{35} - 16q^{37} + 8q^{39} - 4q^{41} - 4q^{47} - 20q^{49} - 8q^{53} + 8q^{55} - 8q^{57} + 12q^{59} - 16q^{61} - 36q^{65} - 24q^{67} + 4q^{69} + 12q^{71} + 24q^{73} - 8q^{75} - 16q^{77} + 12q^{79} - 28q^{81} + 8q^{83} - 36q^{85} - 20q^{89} + 16q^{91} - 52q^{97} + 4q^{99} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(2004, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(167, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(334, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(501, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(668, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1002, [\chi])\)\(^{\oplus 2}\)