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Properties

Label 1075.6.bj
Level $1075$
Weight $6$
Character orbit 1075.bj
Rep. character $\chi_{1075}(4,\cdot)$
Character field $\Q(\zeta_{70})$
Dimension $13152$
Sturm bound $660$

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Defining parameters

Level: \( N \) \(=\) \( 1075 = 5^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1075.bj (of order \(70\) and degree \(24\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1075 \)
Character field: \(\Q(\zeta_{70})\)
Sturm bound: \(660\)

Dimensions

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

Total New Old
Modular forms 13248 13248 0
Cusp forms 13152 13152 0
Eisenstein series 96 96 0

Trace form

\( 13152 q - 25 q^{2} - 25 q^{3} - 8751 q^{4} - 42 q^{5} + 92 q^{6} - 25 q^{8} - 44079 q^{9} + O(q^{10}) \) \( 13152 q - 25 q^{2} - 25 q^{3} - 8751 q^{4} - 42 q^{5} + 92 q^{6} - 25 q^{8} - 44079 q^{9} - 524 q^{10} + 459 q^{11} - 25 q^{12} - 25 q^{13} + 465 q^{14} + 1456 q^{15} + 146521 q^{16} + 1885 q^{17} - 8171 q^{19} - 1422 q^{20} + 3630 q^{21} - 25 q^{22} + 21955 q^{23} + 28072 q^{24} + 7832 q^{25} - 32360 q^{26} - 25 q^{27} + 25575 q^{28} + 11163 q^{29} + 49891 q^{30} - 15 q^{31} - 31125 q^{33} - 9135 q^{34} + 117052 q^{35} - 4140100 q^{36} - 60 q^{37} + 86005 q^{38} - 7799 q^{39} + 151032 q^{40} - 15 q^{41} + 265600 q^{42} - 14818 q^{44} - 371139 q^{45} - 11319 q^{46} + 15365 q^{47} + 281225 q^{48} - 30873580 q^{49} + 541562 q^{50} - 242288 q^{51} + 378485 q^{52} - 89475 q^{53} + 115529 q^{54} - 33270 q^{55} + 232318 q^{56} - 291855 q^{58} - 97443 q^{59} - 605904 q^{60} - 87073 q^{61} + 335135 q^{62} + 446150 q^{63} - 1579087 q^{64} - 208978 q^{65} + 245741 q^{66} - 25 q^{67} - 145707 q^{69} + 181118 q^{70} + 291349 q^{71} + 599205 q^{72} - 677605 q^{73} - 172588 q^{74} - 67373 q^{75} + 95832 q^{76} + 420150 q^{77} + 1070815 q^{78} - 5780 q^{79} - 162418 q^{80} + 3491409 q^{81} - 1067355 q^{83} + 326406 q^{84} - 1739444 q^{85} - 148672 q^{86} + 820970 q^{87} - 446745 q^{88} - 97896 q^{89} - 1127583 q^{90} + 384586 q^{91} + 2461050 q^{92} + 501533 q^{94} - 1014074 q^{95} - 1501469 q^{96} - 25 q^{97} + 6870 q^{98} - 651246 q^{99} + O(q^{100}) \)

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.