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Properties

Label 1045.4.bu
Level $1045$
Weight $4$
Character orbit 1045.bu
Rep. character $\chi_{1045}(49,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $2848$
Sturm bound $480$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1045.bu (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1045 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(480\)

Dimensions

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

Total New Old
Modular forms 2912 2912 0
Cusp forms 2848 2848 0
Eisenstein series 64 64 0

Trace form

\( 2848 q - 1414 q^{4} + 5 q^{5} + 58 q^{6} - 3138 q^{9} + O(q^{10}) \) \( 2848 q - 1414 q^{4} + 5 q^{5} + 58 q^{6} - 3138 q^{9} + 24 q^{10} - 60 q^{11} - 26 q^{14} + 129 q^{15} + 5466 q^{16} + 8 q^{19} + 1080 q^{20} + 1220 q^{21} - 946 q^{24} + 137 q^{25} + 164 q^{26} + 690 q^{29} + 198 q^{30} - 24 q^{31} + 48 q^{34} - 773 q^{35} + 12020 q^{36} + 192 q^{39} - 126 q^{40} - 652 q^{41} + 2940 q^{44} + 312 q^{45} - 2888 q^{46} + 34420 q^{49} - 3070 q^{50} - 2550 q^{51} - 6892 q^{54} - 35 q^{55} - 6192 q^{56} - 962 q^{59} + 694 q^{60} - 414 q^{61} + 47760 q^{64} + 3196 q^{65} + 2764 q^{66} + 5940 q^{69} + 1818 q^{70} - 1574 q^{71} - 1982 q^{74} - 3552 q^{75} + 3828 q^{76} + 3154 q^{79} - 5803 q^{80} + 23170 q^{81} - 248 q^{84} - 5915 q^{85} + 5294 q^{86} - 1300 q^{89} + 683 q^{90} - 4516 q^{91} - 36048 q^{94} + 788 q^{95} + 24772 q^{96} - 5884 q^{99} + O(q^{100}) \)

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.