↑

Properties

Label 1075.6.u
Level $1075$
Weight $6$
Character orbit 1075.u
Rep. character $\chi_{1075}(6,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $4384$
Sturm bound $660$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1075 = 5^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1075.u (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1075 \)
Character field: \(\Q(\zeta_{15})\)
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

\( 4384 q - 12 q^{2} - 3 q^{3} - 17484 q^{4} - 26 q^{5} + 61 q^{6} - 126 q^{7} + 244 q^{8} + 44061 q^{9} + O(q^{10}) \) \( 4384 q - 12 q^{2} - 3 q^{3} - 17484 q^{4} - 26 q^{5} + 61 q^{6} - 126 q^{7} + 244 q^{8} + 44061 q^{9} + 312 q^{10} - 486 q^{11} - 245 q^{12} - 1051 q^{13} - 99 q^{14} - 688 q^{15} - 284916 q^{16} - 576 q^{17} + 2878 q^{18} - 257 q^{19} + 470 q^{20} + 1446 q^{21} + 5828 q^{22} + 1059 q^{23} + 19362 q^{24} + 2842 q^{25} + 32504 q^{26} - 11088 q^{27} - 10563 q^{28} - 5841 q^{29} + 19244 q^{30} - 3 q^{31} - 1224 q^{32} + 29559 q^{33} - 9187 q^{34} + 28622 q^{35} + 651485 q^{36} - 3 q^{37} + 20346 q^{38} + 16528 q^{39} - 26926 q^{40} - 12 q^{41} + 311464 q^{42} + 2952 q^{43} - 2378 q^{44} - 106864 q^{45} + 11493 q^{46} + 126010 q^{47} + 154495 q^{48} - 5154242 q^{49} + 305063 q^{50} - 293116 q^{51} + 12968 q^{52} + 96817 q^{53} + 9712 q^{54} - 34084 q^{55} - 56214 q^{56} - 28270 q^{57} + 87610 q^{58} + 206328 q^{59} - 21933 q^{60} - 18313 q^{61} - 123589 q^{62} + 236895 q^{63} - 4611724 q^{64} - 281592 q^{65} - 150797 q^{66} + 136925 q^{67} + 455912 q^{68} - 41907 q^{69} + 284460 q^{70} - 66043 q^{71} - 204413 q^{72} - 15793 q^{73} + 86170 q^{74} - 178378 q^{75} + 351800 q^{76} - 97876 q^{77} - 737264 q^{78} - 5747 q^{79} + 41296 q^{80} + 3490935 q^{81} + 1972152 q^{82} - 88748 q^{83} + 77202 q^{84} - 349636 q^{85} + 148360 q^{86} - 1642574 q^{87} - 476236 q^{88} - 189624 q^{89} - 627078 q^{90} - 31657 q^{91} - 421611 q^{92} - 10912 q^{93} + 231424 q^{94} - 358396 q^{95} - 578938 q^{96} - 564444 q^{97} + 354823 q^{98} + 101144 q^{99} + O(q^{100}) \)

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.