Properties

Label 1045.4.s
Level $1045$
Weight $4$
Character orbit 1045.s
Rep. character $\chi_{1045}(164,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $712$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1045.s (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1045 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1045, [\chi])\).

Total New Old
Modular forms 728 728 0
Cusp forms 712 712 0
Eisenstein series 16 16 0

Trace form

\( 712 q + 1404 q^{4} + 6 q^{5} - 3136 q^{9} + O(q^{10}) \) \( 712 q + 1404 q^{4} + 6 q^{5} - 3136 q^{9} - 36 q^{11} - 132 q^{14} - 78 q^{15} - 5476 q^{16} + 1232 q^{20} - 58 q^{25} - 1272 q^{26} - 12 q^{34} + 12736 q^{36} + 386 q^{44} - 104 q^{45} + 33792 q^{49} + 86 q^{55} + 1644 q^{59} - 1794 q^{60} - 46448 q^{64} - 1710 q^{66} + 204 q^{70} - 828 q^{71} + 6138 q^{80} - 27876 q^{81} + 3648 q^{86} + 3840 q^{89} - 1704 q^{91} - 2814 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1045, [\chi])\) into newform subspaces

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