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Properties

Label 1008.2.du
Level $1008$
Weight $2$
Character orbit 1008.du
Rep. character $\chi_{1008}(37,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $312$
Sturm bound $384$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.du (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(384\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1008, [\chi])\).

Total New Old
Modular forms 800 328 472
Cusp forms 736 312 424
Eisenstein series 64 16 48

Trace form

\( 312 q + 2 q^{2} - 4 q^{4} + 2 q^{5} - 4 q^{8} + O(q^{10}) \) \( 312 q + 2 q^{2} - 4 q^{4} + 2 q^{5} - 4 q^{8} + 4 q^{10} - 2 q^{11} - 8 q^{13} - 8 q^{14} + 4 q^{17} - 2 q^{19} + 24 q^{20} + 12 q^{22} + 2 q^{26} + 10 q^{28} + 24 q^{29} + 20 q^{31} - 8 q^{32} + 32 q^{34} + 26 q^{35} - 10 q^{37} + 22 q^{38} - 54 q^{40} - 16 q^{43} + 34 q^{44} + 44 q^{47} - 8 q^{49} + 56 q^{50} + 28 q^{52} + 10 q^{53} - 16 q^{56} + 26 q^{58} - 14 q^{59} - 2 q^{61} + 116 q^{62} - 16 q^{64} + 4 q^{65} + 14 q^{67} - 4 q^{68} + 28 q^{70} + 22 q^{74} - 20 q^{76} + 18 q^{77} - 4 q^{79} - 48 q^{80} + 22 q^{82} - 32 q^{83} + 12 q^{85} - 26 q^{88} - 16 q^{91} + 116 q^{92} + 66 q^{94} + 28 q^{95} - 16 q^{97} - 96 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

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

Decomposition of \(S_{2}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

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