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Properties

Label 1008.4.ec
Level $1008$
Weight $4$
Character orbit 1008.ec
Rep. character $\chi_{1008}(19,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $952$
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.ec (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
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 2336 968 1368
Cusp forms 2272 952 1320
Eisenstein series 64 16 48

Trace form

\( 952 q + 2 q^{2} - 12 q^{4} + 6 q^{5} - 8 q^{7} - 76 q^{8} + O(q^{10}) \) \( 952 q + 2 q^{2} - 12 q^{4} + 6 q^{5} - 8 q^{7} - 76 q^{8} + 12 q^{10} + 22 q^{11} - 220 q^{14} - 32 q^{16} + 12 q^{17} - 6 q^{19} - 276 q^{22} - 324 q^{23} + 6 q^{26} - 30 q^{28} + 408 q^{29} + 492 q^{32} + 26 q^{35} - 10 q^{37} + 6 q^{38} - 2346 q^{40} + 800 q^{43} + 1138 q^{44} + 380 q^{46} - 8 q^{49} - 2088 q^{50} - 4812 q^{52} + 378 q^{53} - 664 q^{56} - 1918 q^{58} - 2058 q^{59} - 6 q^{61} - 624 q^{64} + 4 q^{65} - 1130 q^{67} + 3036 q^{68} + 2420 q^{70} + 464 q^{71} + 1402 q^{74} - 682 q^{77} + 3768 q^{80} - 5274 q^{82} - 508 q^{85} - 1392 q^{86} + 246 q^{88} + 416 q^{91} + 5468 q^{92} + 7014 q^{94} - 5796 q^{98} + O(q^{100}) \)

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

\( S_{4}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)