Properties

Label 1075.6.bb
Level $1075$
Weight $6$
Character orbit 1075.bb
Rep. character $\chi_{1075}(79,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $4384$
Sturm bound $660$

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Defining parameters

Level: \( N \) \(=\) \( 1075 = 5^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1075.bb (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1075 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(660\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(1075, [\chi])\).

Total New Old
Modular forms 4416 4416 0
Cusp forms 4384 4384 0
Eisenstein series 32 32 0

Trace form

\( 4384 q - 20 q^{2} - 5 q^{3} + 17460 q^{4} - 26 q^{5} - 67 q^{6} - 20 q^{8} - 44067 q^{9} + O(q^{10}) \) \( 4384 q - 20 q^{2} - 5 q^{3} + 17460 q^{4} - 26 q^{5} - 67 q^{6} - 20 q^{8} - 44067 q^{9} + 248 q^{10} + 462 q^{11} - 5 q^{12} - 5 q^{13} + 93 q^{14} + 680 q^{15} - 270116 q^{16} - 960 q^{17} - 257 q^{19} + 1570 q^{20} - 1470 q^{21} - 20 q^{22} - 10995 q^{23} + 18262 q^{24} - 7294 q^{25} - 32520 q^{26} - 20 q^{27} + 5115 q^{28} - 5841 q^{29} - 17572 q^{30} - 3 q^{31} - 45865 q^{33} - 9315 q^{34} - 38510 q^{35} + 747101 q^{36} - 5 q^{37} - 43020 q^{38} + 18472 q^{39} + 31050 q^{40} - 12 q^{41} + 324020 q^{42} - 2890 q^{44} + 56512 q^{45} - 11499 q^{46} + 15370 q^{47} + 280765 q^{48} + 5141246 q^{49} + 159881 q^{50} + 293052 q^{51} - 189260 q^{52} - 17895 q^{53} + 6284 q^{54} + 71622 q^{55} + 60304 q^{56} + 145910 q^{58} + 206328 q^{59} + 162265 q^{60} + 18307 q^{61} - 38765 q^{62} - 181075 q^{63} + 4138100 q^{64} - 151824 q^{65} + 181895 q^{66} - 5 q^{67} - 39963 q^{69} + 72060 q^{70} + 66037 q^{71} - 295975 q^{72} - 18985 q^{73} + 86042 q^{74} + 191206 q^{75} - 347720 q^{76} + 84030 q^{77} + 1070820 q^{78} - 5747 q^{79} + 54082 q^{80} + 3489963 q^{81} - 74010 q^{83} - 123050 q^{84} + 375964 q^{85} - 148372 q^{86} - 487190 q^{87} - 446740 q^{88} - 189624 q^{89} - 345886 q^{90} + 31651 q^{91} + 998655 q^{92} + 230912 q^{94} + 31384 q^{95} + 603892 q^{96} - 20 q^{97} - 580715 q^{98} + 103088 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(1075, [\chi])\) into newform subspaces

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