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Properties

Label 775.3.ba
Level $775$
Weight $3$
Character orbit 775.ba
Rep. character $\chi_{775}(89,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $632$
Sturm bound $240$

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Defining parameters

Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 775.ba (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{10})\)
Sturm bound: \(240\)

Dimensions

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

Total New Old
Modular forms 648 648 0
Cusp forms 632 632 0
Eisenstein series 16 16 0

Trace form

\( 632 q - 5 q^{2} - 5 q^{3} + 311 q^{4} - 2 q^{5} + 20 q^{6} - 20 q^{7} - 40 q^{8} - 483 q^{9} + O(q^{10}) \) \( 632 q - 5 q^{2} - 5 q^{3} + 311 q^{4} - 2 q^{5} + 20 q^{6} - 20 q^{7} - 40 q^{8} - 483 q^{9} + 14 q^{10} - 5 q^{11} - 45 q^{12} - 5 q^{13} + 8 q^{14} - 5 q^{15} - 605 q^{16} - 5 q^{17} + 65 q^{18} - q^{19} + 187 q^{20} - 80 q^{22} - 10 q^{23} - 55 q^{24} - 116 q^{25} + 40 q^{27} - 125 q^{28} + 55 q^{30} - 73 q^{31} - 5 q^{33} - 25 q^{34} + 68 q^{35} + 1001 q^{36} - 205 q^{37} + 30 q^{39} - 373 q^{40} + 14 q^{41} + 240 q^{42} - 90 q^{43} + 4 q^{45} + 155 q^{46} - 210 q^{47} - 250 q^{48} + 1076 q^{49} - 390 q^{50} - 100 q^{51} - 40 q^{52} - 195 q^{53} - 5 q^{54} + 415 q^{55} + 146 q^{56} + 440 q^{57} - 5 q^{58} - 101 q^{59} - 125 q^{60} - 70 q^{62} - 15 q^{63} + 1274 q^{64} - 125 q^{65} + 320 q^{66} - 370 q^{67} - 880 q^{68} + 550 q^{69} - 244 q^{70} - 71 q^{71} - 25 q^{73} - 10 q^{74} - 20 q^{75} + 282 q^{76} + 135 q^{77} - 200 q^{78} - 155 q^{79} + 107 q^{80} - 1058 q^{81} - 480 q^{82} + 610 q^{83} + 220 q^{84} - 15 q^{85} + 1045 q^{86} - 325 q^{87} + 70 q^{89} + 1229 q^{90} + 240 q^{91} + 1350 q^{92} + 650 q^{93} + 123 q^{94} + 208 q^{95} - 180 q^{96} + 180 q^{97} - 575 q^{98} + O(q^{100}) \)

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.