↑

Properties

Label 1075.6.h
Level $1075$
Weight $6$
Character orbit 1075.h
Rep. character $\chi_{1075}(216,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $2104$
Sturm bound $660$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 1075 = 5^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1075.h (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 25 \)
Character field: \(\Q(\zeta_{5})\)
Sturm bound: \(660\)

Dimensions

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

Total New Old
Modular forms 2208 2104 104
Cusp forms 2192 2104 88
Eisenstein series 16 0 16

Trace form

\( 2104 q + 8 q^{2} - 4 q^{3} - 8448 q^{4} - 216 q^{5} - 144 q^{6} + 152 q^{7} + 1122 q^{8} - 43054 q^{9} + O(q^{10}) \) \( 2104 q + 8 q^{2} - 4 q^{3} - 8448 q^{4} - 216 q^{5} - 144 q^{6} + 152 q^{7} + 1122 q^{8} - 43054 q^{9} + 734 q^{10} - 968 q^{11} + 384 q^{12} + 1624 q^{13} + 1180 q^{14} + 2332 q^{15} - 136192 q^{16} - 2588 q^{17} - 8416 q^{18} + 496 q^{20} + 2580 q^{21} + 1946 q^{22} + 4540 q^{23} + 27648 q^{24} + 17532 q^{25} + 3428 q^{26} - 7900 q^{27} - 39868 q^{28} - 9896 q^{29} - 16352 q^{30} + 17268 q^{31} - 47508 q^{32} + 13292 q^{33} + 20648 q^{34} - 24 q^{35} - 707776 q^{36} + 101548 q^{37} + 41238 q^{38} - 4296 q^{39} - 5608 q^{40} - 11122 q^{41} + 11440 q^{42} - 38720 q^{44} - 19230 q^{45} - 40416 q^{46} + 50588 q^{47} + 104928 q^{48} + 5183712 q^{49} - 40360 q^{50} + 81856 q^{52} + 169376 q^{53} - 46656 q^{54} - 60920 q^{55} - 207168 q^{56} - 637924 q^{57} + 252680 q^{58} + 2142 q^{59} - 29022 q^{60} + 150824 q^{61} - 105930 q^{62} + 13916 q^{63} - 2000670 q^{64} + 289896 q^{65} + 107302 q^{66} - 384050 q^{67} - 624028 q^{68} + 383072 q^{69} - 357956 q^{70} + 69782 q^{71} + 852462 q^{72} - 129944 q^{73} + 531068 q^{74} + 105642 q^{75} - 144080 q^{76} + 382708 q^{77} - 173540 q^{78} + 113868 q^{79} + 858430 q^{80} - 4044724 q^{81} - 714228 q^{82} - 377478 q^{83} - 813580 q^{84} - 1247724 q^{85} - 73960 q^{86} - 252566 q^{87} - 1113094 q^{88} - 175580 q^{89} - 559070 q^{90} + 393752 q^{91} - 887840 q^{92} + 1190900 q^{93} - 171100 q^{94} - 177844 q^{95} - 592864 q^{96} + 842382 q^{97} + 1629304 q^{98} + 1566756 q^{99} + O(q^{100}) \)

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.

Decomposition of \(S_{6}^{\mathrm{old}}(1075, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(1075, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)