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Properties

Label 1008.4.v
Level $1008$
Weight $4$
Character orbit 1008.v
Rep. character $\chi_{1008}(323,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $288$
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.v (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 48 \)
Character field: \(\Q(i)\)
Sturm bound: \(768\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1008, [\chi])\).

Total New Old
Modular forms 1168 288 880
Cusp forms 1136 288 848
Eisenstein series 32 0 32

Trace form

\( 288 q + O(q^{10}) \) \( 288 q + 240 q^{10} + 408 q^{16} + 96 q^{19} + 864 q^{22} + 1392 q^{34} - 1728 q^{43} + 2832 q^{46} + 14112 q^{49} - 2016 q^{52} + 1152 q^{55} + 888 q^{58} - 3648 q^{61} - 816 q^{67} - 1008 q^{70} - 1392 q^{76} + 4560 q^{82} + 960 q^{85} + 7512 q^{88} + 8928 q^{94} + O(q^{100}) \)

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

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