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Properties

Label 1075.6.bi
Level $1075$
Weight $6$
Character orbit 1075.bi
Rep. character $\chi_{1075}(37,\cdot)$
Character field $\Q(\zeta_{60})$
Dimension $8768$
Sturm bound $660$

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Defining parameters

Level: \( N \) \(=\) \( 1075 = 5^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1075.bi (of order \(60\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1075 \)
Character field: \(\Q(\zeta_{60})\)
Sturm bound: \(660\)

Dimensions

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

Total New Old
Modular forms 8832 8832 0
Cusp forms 8768 8768 0
Eisenstein series 64 64 0

Trace form

\( 8768 q - 24 q^{3} - 40 q^{4} - 24 q^{5} - 6 q^{6} - 378 q^{7} - 10 q^{9} + O(q^{10}) \) \( 8768 q - 24 q^{3} - 40 q^{4} - 24 q^{5} - 6 q^{6} - 378 q^{7} - 10 q^{9} + 560 q^{10} - 24 q^{11} + 702 q^{12} + 1040 q^{13} - 10 q^{14} - 8 q^{15} + 554984 q^{16} - 1536 q^{17} - 11214 q^{18} + 26310 q^{19} - 6168 q^{20} - 24 q^{21} - 9936 q^{23} - 4452 q^{25} - 48 q^{26} - 28632 q^{28} + 42510 q^{29} - 34356 q^{30} - 6 q^{31} - 24882 q^{33} - 30 q^{34} + 9824 q^{35} + 1390394 q^{36} - 24 q^{37} - 51750 q^{38} - 4140 q^{40} - 24 q^{41} + 15952 q^{43} - 103500 q^{44} - 18 q^{46} - 30388 q^{47} + 44016 q^{48} + 8520 q^{50} - 156732 q^{52} - 78938 q^{53} - 132380 q^{54} + 174150 q^{55} - 4102 q^{56} - 28270 q^{57} - 233408 q^{58} - 675080 q^{59} + 312996 q^{60} - 18 q^{61} - 42966 q^{62} - 653016 q^{63} - 816680 q^{64} + 31098 q^{66} + 136920 q^{67} - 406904 q^{68} - 30 q^{69} - 18 q^{71} - 1101108 q^{72} - 285510 q^{73} - 12336 q^{76} - 29118 q^{77} + 325780 q^{78} + 75270 q^{79} + 382242 q^{80} - 6980910 q^{81} - 162758 q^{83} - 40 q^{84} - 12 q^{86} - 277620 q^{87} + 229320 q^{89} + 1233572 q^{90} - 18 q^{91} - 577060 q^{92} - 419172 q^{93} + 571404 q^{95} + 37242 q^{96} + 564400 q^{97} - 20568 q^{98} + O(q^{100}) \)

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.