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Properties

Label 1008.3.dt
Level $1008$
Weight $3$
Character orbit 1008.dt
Rep. character $\chi_{1008}(163,\cdot)$
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.dt (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

\( 632 q + 2 q^{2} + 4 q^{4} + 2 q^{5} - 8 q^{7} - 4 q^{8} + O(q^{10}) \) \( 632 q + 2 q^{2} + 4 q^{4} + 2 q^{5} - 8 q^{7} - 4 q^{8} + 16 q^{10} + 18 q^{11} - 8 q^{13} + 12 q^{14} + 4 q^{17} - 2 q^{19} + 88 q^{20} + 4 q^{22} - 60 q^{23} + 2 q^{26} + 58 q^{28} - 24 q^{29} - 88 q^{32} - 152 q^{34} + 2 q^{35} - 50 q^{37} + 142 q^{38} + 202 q^{40} - 104 q^{43} - 126 q^{44} - 76 q^{46} - 8 q^{49} - 272 q^{50} - 188 q^{52} - 78 q^{53} - 16 q^{55} + 48 q^{56} + 242 q^{58} + 66 q^{59} - 2 q^{61} + 132 q^{62} + 16 q^{64} + 4 q^{65} - 130 q^{67} + 68 q^{68} + 160 q^{70} + 528 q^{71} + 350 q^{74} - 68 q^{76} - 94 q^{77} + 208 q^{80} - 254 q^{82} + 488 q^{83} + 92 q^{85} + 196 q^{86} - 234 q^{88} - 296 q^{91} + 788 q^{92} + 114 q^{94} - 16 q^{97} + 220 q^{98} + O(q^{100}) \)

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

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