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Properties

Label 1008.3.ej
Level $1008$
Weight $3$
Character orbit 1008.ej
Rep. character $\chi_{1008}(325,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $632$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1008.ej (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1008, [\chi])\).

Total New Old
Modular forms 1568 648 920
Cusp forms 1504 632 872
Eisenstein series 64 16 48

Trace form

\( 632 q + 2 q^{2} + 4 q^{4} + 6 q^{5} + 20 q^{8} + O(q^{10}) \) \( 632 q + 2 q^{2} + 4 q^{4} + 6 q^{5} + 20 q^{8} - 60 q^{10} - 14 q^{11} - 4 q^{14} + 12 q^{17} - 6 q^{19} - 68 q^{22} + 6 q^{26} - 126 q^{28} + 40 q^{29} - 12 q^{31} + 92 q^{32} + 2 q^{35} + 46 q^{37} + 6 q^{38} + 54 q^{40} + 88 q^{43} - 46 q^{44} - 108 q^{46} + 12 q^{47} - 8 q^{49} + 40 q^{50} + 228 q^{52} - 78 q^{53} - 344 q^{56} - 110 q^{58} - 186 q^{59} - 6 q^{61} + 112 q^{64} + 4 q^{65} + 158 q^{67} + 396 q^{68} + 508 q^{70} - 38 q^{74} + 102 q^{77} - 4 q^{79} + 312 q^{80} + 750 q^{82} - 108 q^{85} + 408 q^{86} + 230 q^{88} - 104 q^{91} + 316 q^{92} - 618 q^{94} - 380 q^{95} + 196 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)