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Properties

Label 1008.3.u
Level $1008$
Weight $3$
Character orbit 1008.u
Rep. character $\chi_{1008}(181,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $316$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1008.u (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 112 \)
Character field: \(\Q(i)\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1008, [\chi])\).

Total New Old
Modular forms 784 324 460
Cusp forms 752 316 436
Eisenstein series 32 8 24

Trace form

\( 316 q + 4 q^{2} - 10 q^{4} - 8 q^{8} + O(q^{10}) \) \( 316 q + 4 q^{2} - 10 q^{4} - 8 q^{8} + 20 q^{11} - 14 q^{14} - 6 q^{16} + 2 q^{22} + 120 q^{28} + 20 q^{29} + 184 q^{32} + 4 q^{35} - 52 q^{37} + 44 q^{43} - 14 q^{44} - 168 q^{46} - 4 q^{49} - 238 q^{50} + 84 q^{53} + 98 q^{56} - 298 q^{58} + 254 q^{64} + 8 q^{65} + 268 q^{67} - 136 q^{70} - 286 q^{74} - 96 q^{77} - 8 q^{79} + 96 q^{85} + 6 q^{86} + 358 q^{88} - 196 q^{91} - 640 q^{92} - 760 q^{95} + 356 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

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

Decomposition of \(S_{3}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

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