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Properties

Label 1008.2.z
Level $1008$
Weight $2$
Character orbit 1008.z
Rep. character $\chi_{1008}(253,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $120$
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.z (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 16 \)
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 400 120 280
Cusp forms 368 120 248
Eisenstein series 32 0 32

Trace form

\( 120 q - 2 q^{4} + O(q^{10}) \) \( 120 q - 2 q^{4} - 8 q^{10} - 4 q^{11} - 2 q^{14} + 10 q^{16} + 16 q^{19} + 28 q^{20} - 14 q^{22} + 52 q^{26} - 8 q^{29} + 28 q^{34} - 8 q^{37} - 56 q^{38} + 20 q^{40} + 36 q^{43} - 26 q^{44} - 48 q^{46} - 120 q^{49} - 86 q^{50} - 16 q^{52} + 8 q^{53} + 14 q^{56} + 34 q^{58} + 24 q^{59} - 32 q^{61} + 12 q^{62} - 50 q^{64} - 16 q^{65} + 4 q^{67} + 104 q^{68} - 24 q^{70} + 22 q^{74} + 80 q^{76} + 8 q^{77} - 72 q^{79} + 68 q^{80} + 44 q^{82} - 40 q^{83} + 32 q^{85} - 2 q^{86} - 94 q^{88} - 100 q^{92} - 52 q^{94} - 64 q^{95} + O(q^{100}) \)

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

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)