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Properties

Label 1075.6.bq
Level $1075$
Weight $6$
Character orbit 1075.bq
Rep. character $\chi_{1075}(2,\cdot)$
Character field $\Q(\zeta_{140})$
Dimension $26304$
Sturm bound $660$

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Defining parameters

Level: \( N \) \(=\) \( 1075 = 5^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1075.bq (of order \(140\) and degree \(48\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1075 \)
Character field: \(\Q(\zeta_{140})\)
Sturm bound: \(660\)

Dimensions

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

Total New Old
Modular forms 26496 26496 0
Cusp forms 26304 26304 0
Eisenstein series 192 192 0

Trace form

\( 26304 q - 56 q^{2} - 56 q^{3} - 50 q^{4} - 56 q^{5} - 72 q^{6} - 56 q^{8} - 50 q^{9} + O(q^{10}) \) \( 26304 q - 56 q^{2} - 56 q^{3} - 50 q^{4} - 56 q^{5} - 72 q^{6} - 56 q^{8} - 50 q^{9} - 1176 q^{10} - 30 q^{11} + 392 q^{12} - 2660 q^{13} - 50 q^{14} - 40 q^{15} - 277534 q^{16} + 3016 q^{17} + 3346 q^{18} - 70 q^{19} - 56 q^{20} - 30 q^{21} - 56 q^{22} + 19816 q^{23} - 4484 q^{25} - 112 q^{26} - 56 q^{27} + 14280 q^{28} - 99330 q^{29} + 157234 q^{30} - 30 q^{31} - 33796 q^{32} - 41384 q^{33} - 70 q^{34} - 80832 q^{35} - 8358856 q^{36} + 14952 q^{38} - 70 q^{39} + 90832 q^{40} - 30 q^{41} - 380092 q^{43} - 103580 q^{44} - 56 q^{45} - 42 q^{46} - 113688 q^{47} + 286216 q^{48} - 112 q^{51} + 112192 q^{52} - 2628 q^{53} - 132390 q^{54} - 56 q^{55} + 8162 q^{56} + 53568 q^{57} + 466760 q^{58} + 337470 q^{59} + 8164 q^{60} - 42 q^{61} - 261800 q^{62} + 235242 q^{63} + 2041550 q^{64} + 114268 q^{65} + 155490 q^{66} - 342360 q^{67} - 303192 q^{68} - 70 q^{69} + 821604 q^{70} - 42 q^{71} + 495516 q^{72} + 1601838 q^{73} - 56 q^{75} - 112 q^{76} + 482076 q^{77} + 534476 q^{78} + 75160 q^{79} - 6980934 q^{81} - 196812 q^{82} - 1309520 q^{83} - 50 q^{84} - 36 q^{86} + 45588 q^{87} - 504 q^{88} - 535220 q^{89} - 200340 q^{90} - 42 q^{91} - 2862924 q^{92} - 70 q^{94} + 1308484 q^{95} + 143202 q^{96} + 705500 q^{97} + 237034 q^{98} + O(q^{100}) \)

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.