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Properties

Label 1045.6.bu
Level $1045$
Weight $6$
Character orbit 1045.bu
Rep. character $\chi_{1045}(49,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $4768$
Sturm bound $720$

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Defining parameters

Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.bu (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1045 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(720\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1045, [\chi])\).

Total New Old
Modular forms 4832 4832 0
Cusp forms 4768 4768 0
Eisenstein series 64 64 0

Trace form

\( 4768 q - 9478 q^{4} - 25 q^{5} + 250 q^{6} - 47634 q^{9} + O(q^{10}) \) \( 4768 q - 9478 q^{4} - 25 q^{5} + 250 q^{6} - 47634 q^{9} + 120 q^{10} + 264 q^{11} - 1454 q^{14} + 1365 q^{15} + 149370 q^{16} + 1920 q^{19} - 27576 q^{20} - 29212 q^{21} - 898 q^{24} - 2291 q^{25} + 37412 q^{26} - 20190 q^{29} - 17154 q^{30} - 24 q^{31} + 240 q^{34} + 4213 q^{35} + 701348 q^{36} + 1920 q^{39} - 3142 q^{40} + 32096 q^{41} - 35628 q^{44} + 87660 q^{45} + 15816 q^{46} + 2843080 q^{49} + 29042 q^{50} + 133290 q^{51} + 16580 q^{54} - 27945 q^{55} - 192432 q^{56} - 11270 q^{59} + 138862 q^{60} - 75368 q^{61} + 4367088 q^{64} - 162032 q^{65} - 413132 q^{66} + 126684 q^{69} + 91162 q^{70} + 108322 q^{71} - 95894 q^{74} + 356832 q^{75} - 422188 q^{76} - 249646 q^{79} + 530693 q^{80} + 3674434 q^{81} + 1685320 q^{84} + 181884 q^{85} - 681250 q^{86} + 71924 q^{89} + 470243 q^{90} - 71964 q^{91} + 1274528 q^{94} - 561586 q^{95} + 241828 q^{96} + 735998 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(1045, [\chi])\) into newform subspaces

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