Properties

Label 1008.2.z
Level 1008
Weight 2
Character orbit 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

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

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database