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Properties

Label 1008.2.x
Level $1008$
Weight $2$
Character orbit 1008.x
Rep. character $\chi_{1008}(307,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $156$
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.x (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(i)\)
Sturm bound: \(384\)

Dimensions

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

Total New Old
Modular forms 400 164 236
Cusp forms 368 156 212
Eisenstein series 32 8 24

Trace form

\( 156 q + 4 q^{2} - 2 q^{4} - 4 q^{7} - 8 q^{8} + O(q^{10}) \) \( 156 q + 4 q^{2} - 2 q^{4} - 4 q^{7} - 8 q^{8} + 14 q^{14} - 6 q^{16} - 26 q^{22} + 16 q^{23} - 8 q^{28} - 4 q^{29} + 24 q^{32} - 20 q^{35} - 12 q^{37} - 22 q^{44} + 8 q^{46} - 4 q^{49} + 22 q^{50} - 4 q^{53} + 50 q^{56} - 6 q^{58} - 50 q^{64} + 8 q^{65} - 32 q^{67} + 32 q^{70} + 72 q^{71} + 62 q^{74} + 16 q^{77} + 16 q^{85} - 62 q^{86} + 38 q^{88} - 28 q^{91} - 48 q^{92} + 4 q^{98} + O(q^{100}) \)

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

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