↑

Properties

Label 273.8.j
Level $273$
Weight $8$
Character orbit 273.j
Rep. character $\chi_{273}(100,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $262$
Sturm bound $298$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 273.j (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 91 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(298\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(273, [\chi])\).

Total New Old
Modular forms 530 262 268
Cusp forms 514 262 252
Eisenstein series 16 0 16

Trace form

\( 262 q - 162 q^{3} - 8448 q^{4} + 1649 q^{7} + 190998 q^{9} + O(q^{10}) \) \( 262 q - 162 q^{3} - 8448 q^{4} + 1649 q^{7} + 190998 q^{9} - 16000 q^{10} + 6056 q^{11} + 13824 q^{12} - 1874 q^{13} + 31568 q^{14} - 580680 q^{16} + 20668 q^{17} - 75762 q^{19} - 41000 q^{20} + 6939 q^{21} + 39086 q^{22} + 36428 q^{23} - 198936 q^{24} - 2113041 q^{25} - 36794 q^{26} - 118098 q^{27} - 258586 q^{28} - 239928 q^{29} - 76087 q^{31} + 729140 q^{32} + 1724408 q^{34} + 248806 q^{35} - 6158592 q^{36} - 621129 q^{37} + 268572 q^{38} + 544536 q^{39} + 2081990 q^{40} - 1187406 q^{41} + 806706 q^{42} + 760372 q^{43} + 451480 q^{44} - 669100 q^{46} + 1188444 q^{47} + 1990656 q^{48} + 1271035 q^{49} + 881506 q^{50} + 532872 q^{51} + 1831136 q^{52} + 756432 q^{53} + 5662854 q^{55} + 11067790 q^{56} - 5428566 q^{57} + 466200 q^{58} - 2279456 q^{59} + 1392768 q^{60} - 8800718 q^{61} + 12134572 q^{62} + 1202121 q^{63} + 86583760 q^{64} + 239208 q^{65} + 4599936 q^{66} + 7994102 q^{67} - 6224284 q^{68} + 6269076 q^{69} + 17730516 q^{70} + 11244994 q^{71} + 2099192 q^{73} + 746784 q^{74} + 6029127 q^{75} + 7102720 q^{76} - 29406730 q^{77} - 8650530 q^{78} + 8005913 q^{79} + 6927608 q^{80} + 139237542 q^{81} + 36596 q^{82} + 20982592 q^{83} + 18686592 q^{84} - 832100 q^{85} + 63440 q^{86} + 17509770 q^{87} - 15462552 q^{88} - 17667872 q^{89} - 11664000 q^{90} + 29373945 q^{91} - 8336308 q^{92} + 9526059 q^{93} - 71353616 q^{94} + 17454252 q^{95} + 26257014 q^{96} - 5272209 q^{97} + 87289274 q^{98} + 4414824 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(273, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{8}^{\mathrm{old}}(273, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(273, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(91, [\chi])\)\(^{\oplus 2}\)