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Properties

Label 1008.4.r
Level $1008$
Weight $4$
Character orbit 1008.r
Rep. character $\chi_{1008}(337,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $216$
Sturm bound $768$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1008, [\chi])\).

Total New Old
Modular forms 1176 216 960
Cusp forms 1128 216 912
Eisenstein series 48 0 48

Trace form

\( 216 q - 20 q^{9} + O(q^{10}) \) \( 216 q - 20 q^{9} + 132 q^{11} - 12 q^{15} + 152 q^{17} - 276 q^{23} - 2700 q^{25} + 756 q^{27} + 36 q^{33} - 840 q^{35} - 252 q^{39} - 20 q^{41} + 1164 q^{47} - 5292 q^{49} - 156 q^{51} - 1708 q^{57} - 1020 q^{59} + 232 q^{65} + 2224 q^{71} - 1656 q^{73} + 1132 q^{75} - 764 q^{81} - 4700 q^{87} - 3760 q^{89} + 2136 q^{93} - 3040 q^{95} - 36 q^{97} - 4540 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

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

Decomposition of \(S_{4}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)