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Properties

Label 1045.4.ce
Level $1045$
Weight $4$
Character orbit 1045.ce
Rep. character $\chi_{1045}(16,\cdot)$
Character field $\Q(\zeta_{45})$
Dimension $5760$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1045.ce (of order \(45\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 209 \)
Character field: \(\Q(\zeta_{45})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 8736 5760 2976
Cusp forms 8544 5760 2784
Eisenstein series 192 0 192

Trace form

\( 5760 q + 12 q^{3} - 180 q^{6} - 288 q^{8} - 180 q^{9} + O(q^{10}) \) \( 5760 q + 12 q^{3} - 180 q^{6} - 288 q^{8} - 180 q^{9} + 72 q^{14} + 36 q^{17} + 1296 q^{18} + 384 q^{22} - 2160 q^{24} - 1272 q^{26} - 876 q^{27} + 3600 q^{29} - 240 q^{30} - 60 q^{31} - 4968 q^{33} + 5880 q^{34} + 780 q^{35} + 6720 q^{36} - 1008 q^{37} + 1584 q^{38} + 1578 q^{41} + 10014 q^{42} + 11286 q^{44} - 3720 q^{47} - 1878 q^{48} + 33000 q^{49} - 600 q^{50} + 4656 q^{51} - 5202 q^{52} - 3528 q^{53} + 2580 q^{54} - 5760 q^{56} + 9024 q^{57} + 5184 q^{58} + 6414 q^{59} - 1800 q^{61} - 1284 q^{62} + 46080 q^{64} + 11220 q^{65} - 2940 q^{66} + 4644 q^{67} - 6384 q^{68} - 3600 q^{69} - 9720 q^{70} + 1500 q^{71} - 13248 q^{72} + 14904 q^{73} + 2184 q^{74} + 1224 q^{76} + 10944 q^{77} - 5280 q^{78} - 5736 q^{81} - 9396 q^{82} + 216 q^{84} + 2040 q^{86} - 3888 q^{88} + 3096 q^{89} + 480 q^{90} - 13734 q^{91} - 4032 q^{93} + 14040 q^{94} - 45024 q^{96} - 10890 q^{97} - 33528 q^{98} + 12504 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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

Decomposition of \(S_{4}^{\mathrm{old}}(1045, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1045, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(209, [\chi])\)\(^{\oplus 2}\)