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Properties

Label 1008.3.en
Level $1008$
Weight $3$
Character orbit 1008.en
Rep. character $\chi_{1008}(43,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1152$
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.en (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
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 1552 1152 400
Cusp forms 1520 1152 368
Eisenstein series 32 0 32

Trace form

\( 1152 q - 12 q^{6} + O(q^{10}) \) \( 1152 q - 12 q^{6} - 120 q^{12} + 84 q^{20} + 32 q^{24} + 192 q^{26} + 96 q^{27} + 216 q^{30} + 32 q^{36} + 504 q^{38} - 384 q^{39} - 336 q^{46} - 52 q^{48} - 4032 q^{49} + 156 q^{50} - 180 q^{58} - 288 q^{59} + 76 q^{60} - 360 q^{62} - 504 q^{64} - 232 q^{66} + 156 q^{68} + 364 q^{72} - 84 q^{74} + 448 q^{75} - 312 q^{76} - 524 q^{78} - 1200 q^{80} + 792 q^{82} + 636 q^{86} + 896 q^{87} + 48 q^{88} - 1336 q^{90} - 228 q^{92} - 96 q^{93} - 544 q^{96} - 256 q^{99} + O(q^{100}) \)

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

\( S_{3}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)