↑

Properties

Label 775.3.cg
Level $775$
Weight $3$
Character orbit 775.cg
Rep. character $\chi_{775}(146,\cdot)$
Character field $\Q(\zeta_{30})$
Dimension $1264$
Sturm bound $240$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 775.cg (of order \(30\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{30})\)
Sturm bound: \(240\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(775, [\chi])\).

Total New Old
Modular forms 1296 1296 0
Cusp forms 1264 1264 0
Eisenstein series 32 32 0

Trace form

\( 1264 q - 2 q^{2} + q^{3} - 626 q^{4} - 7 q^{5} - 5 q^{6} - 26 q^{7} + 42 q^{8} - 475 q^{9} + O(q^{10}) \) \( 1264 q - 2 q^{2} + q^{3} - 626 q^{4} - 7 q^{5} - 5 q^{6} - 26 q^{7} + 42 q^{8} - 475 q^{9} + 28 q^{10} - 4 q^{11} + 69 q^{12} - 4 q^{13} - 30 q^{14} + 110 q^{15} - 1186 q^{16} - 4 q^{17} - 14 q^{18} - 8 q^{19} + 221 q^{20} - 4 q^{21} - 264 q^{22} + 35 q^{23} - 150 q^{24} + 45 q^{25} + 165 q^{26} + 565 q^{27} + 170 q^{28} - 10 q^{29} + 40 q^{30} - 76 q^{31} + 166 q^{32} + 119 q^{33} + 20 q^{34} + 319 q^{35} - 400 q^{36} + 313 q^{37} - 235 q^{38} + 34 q^{39} + 87 q^{40} + 27 q^{41} - 69 q^{42} - 140 q^{43} + 96 q^{44} - 136 q^{45} - 210 q^{46} - 30 q^{47} + 106 q^{48} + 884 q^{49} - 408 q^{50} + 53 q^{51} + 69 q^{52} + 531 q^{53} + 527 q^{55} + 570 q^{56} + 408 q^{57} + 392 q^{59} - 565 q^{60} - 281 q^{62} - 96 q^{63} - 2366 q^{64} + 107 q^{65} - 210 q^{66} - 555 q^{67} - 138 q^{68} - 116 q^{69} - 652 q^{70} - 213 q^{71} - 1335 q^{72} - 8 q^{73} + 245 q^{74} - 1010 q^{75} - 178 q^{76} + 493 q^{78} + 141 q^{79} + 1248 q^{80} + 1287 q^{81} + 381 q^{82} - 66 q^{83} - 149 q^{84} - 85 q^{85} + 380 q^{86} + 343 q^{87} - 644 q^{88} - 10 q^{89} + 922 q^{90} + 1130 q^{92} - 502 q^{93} - 105 q^{94} - 982 q^{95} + 270 q^{96} - 565 q^{97} - 319 q^{98} + 570 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(775, [\chi])\) into newform subspaces

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