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Properties

Label 1075.6.bu
Level $1075$
Weight $6$
Character orbit 1075.bu
Rep. character $\chi_{1075}(3,\cdot)$
Character field $\Q(\zeta_{420})$
Dimension $52608$
Sturm bound $660$

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Defining parameters

Level: \( N \) \(=\) \( 1075 = 5^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1075.bu (of order \(420\) and degree \(96\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1075 \)
Character field: \(\Q(\zeta_{420})\)
Sturm bound: \(660\)

Dimensions

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

Total New Old
Modular forms 52992 52992 0
Cusp forms 52608 52608 0
Eisenstein series 384 384 0

Trace form

\( 52608 q - 112 q^{2} - 88 q^{3} - 100 q^{4} - 88 q^{5} - 36 q^{6} + 210 q^{7} - 112 q^{8} - 130 q^{9} + O(q^{10}) \) \( 52608 q - 112 q^{2} - 88 q^{3} - 100 q^{4} - 88 q^{5} - 36 q^{6} + 210 q^{7} - 112 q^{8} - 130 q^{9} - 672 q^{10} - 60 q^{11} - 1262 q^{12} + 2516 q^{13} - 130 q^{14} - 104 q^{15} - 555068 q^{16} + 1424 q^{17} + 7700 q^{18} - 26450 q^{19} + 6056 q^{20} - 60 q^{21} - 112 q^{22} + 9824 q^{23} + 4340 q^{25} - 176 q^{26} - 112 q^{27} + 14184 q^{28} + 56610 q^{29} - 123046 q^{30} - 78 q^{31} + 33628 q^{32} - 57886 q^{33} - 110 q^{34} - 9936 q^{35} + 8371036 q^{36} - 144 q^{37} - 49050 q^{38} - 140 q^{39} + 4028 q^{40} - 60 q^{41} + 78772 q^{43} + 103220 q^{44} - 112 q^{45} - 66 q^{46} + 30276 q^{47} + 201824 q^{48} - 8688 q^{50} - 224 q^{51} + 156620 q^{52} + 179010 q^{53} + 132240 q^{54} - 174262 q^{55} + 4018 q^{56} + 28158 q^{57} + 233296 q^{58} + 674940 q^{59} - 1040632 q^{60} - 66 q^{61} + 304598 q^{62} + 417606 q^{63} - 2041700 q^{64} - 114436 q^{65} - 248910 q^{66} + 342216 q^{67} + 235656 q^{68} - 110 q^{69} - 821772 q^{70} - 66 q^{71} + 1764204 q^{72} - 1316496 q^{73} - 112 q^{75} + 12112 q^{76} + 746142 q^{77} - 434756 q^{78} - 75340 q^{79} - 382410 q^{80} + 6980826 q^{81} - 1731576 q^{82} + 2107190 q^{83} - 100 q^{84} - 72 q^{86} - 1554084 q^{87} - 1008 q^{88} + 305690 q^{89} - 1342548 q^{90} - 66 q^{91} - 912036 q^{92} + 419004 q^{93} - 140 q^{94} - 2215060 q^{95} - 255054 q^{96} + 1411000 q^{97} - 216634 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

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