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Properties

Label 775.3.bq
Level $775$
Weight $3$
Character orbit 775.bq
Rep. character $\chi_{775}(2,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $1264$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 775.bq (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{20})\)
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

\( 1264 q - 6 q^{2} - 10 q^{3} - 16 q^{5} - 12 q^{6} - 22 q^{7} + 12 q^{8} - 60 q^{9} + O(q^{10}) \) \( 1264 q - 6 q^{2} - 10 q^{3} - 16 q^{5} - 12 q^{6} - 22 q^{7} + 12 q^{8} - 60 q^{9} - 38 q^{10} - 2 q^{11} + 112 q^{12} - 6 q^{13} + 140 q^{14} + 138 q^{15} - 4876 q^{16} - 6 q^{17} + 14 q^{18} - 10 q^{19} + 206 q^{20} - 2 q^{21} + 62 q^{22} + 22 q^{23} + 160 q^{24} - 68 q^{25} - 32 q^{26} + 74 q^{27} + 424 q^{28} - 10 q^{29} + 124 q^{30} - 6 q^{31} + 62 q^{32} + 298 q^{33} + 312 q^{35} - 1756 q^{36} - 26 q^{37} - 356 q^{38} - 10 q^{39} - 378 q^{40} - 2 q^{41} - 1026 q^{42} - 30 q^{43} - 40 q^{44} + 76 q^{45} - 2 q^{46} + 132 q^{47} - 126 q^{48} - 724 q^{50} - 12 q^{51} - 96 q^{52} - 334 q^{53} - 1570 q^{54} - 468 q^{55} + 20 q^{56} + 96 q^{57} + 38 q^{58} + 1070 q^{60} - 12 q^{61} + 300 q^{62} + 84 q^{63} + 276 q^{65} + 286 q^{66} - 346 q^{67} - 248 q^{68} + 1640 q^{69} - 712 q^{70} + 178 q^{71} - 1192 q^{72} - 486 q^{73} + 550 q^{74} + 134 q^{75} + 20 q^{76} + 426 q^{77} + 604 q^{78} + 190 q^{79} - 1202 q^{80} + 2484 q^{81} - 392 q^{82} - 592 q^{83} - 370 q^{84} - 150 q^{85} - 2 q^{86} - 196 q^{87} + 854 q^{88} - 160 q^{89} - 2472 q^{90} - 2 q^{91} + 1458 q^{92} - 130 q^{93} + 1030 q^{94} + 590 q^{95} - 2 q^{96} - 358 q^{97} - 1142 q^{98} + O(q^{100}) \)

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.