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Properties

Label 1008.4.dm
Level $1008$
Weight $4$
Character orbit 1008.dm
Rep. character $\chi_{1008}(155,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1728$
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.dm (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 144 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(768\)

Dimensions

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

Total New Old
Modular forms 2320 1728 592
Cusp forms 2288 1728 560
Eisenstein series 32 0 32

Trace form

\( 1728 q + 60 q^{6} + O(q^{10}) \) \( 1728 q + 60 q^{6} + 312 q^{12} - 924 q^{20} - 736 q^{24} - 264 q^{27} - 48 q^{30} - 1240 q^{36} + 1200 q^{39} + 144 q^{46} + 2444 q^{48} - 42336 q^{49} + 6396 q^{50} + 1188 q^{58} + 6120 q^{59} - 5492 q^{60} - 1080 q^{64} - 1672 q^{66} + 9204 q^{68} + 2596 q^{72} + 5460 q^{74} - 6608 q^{75} + 2232 q^{76} + 484 q^{78} + 2808 q^{82} - 8340 q^{86} + 2576 q^{87} + 4176 q^{88} - 2248 q^{90} + 18924 q^{92} - 4272 q^{93} + 6176 q^{96} + 5312 q^{99} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)