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Properties

Label 775.2.bo
Level $775$
Weight $2$
Character orbit 775.bo
Rep. character $\chi_{775}(81,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $624$
Newform subspaces $1$
Sturm bound $160$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 775.bo (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{15})\)
Newform subspaces: \( 1 \)
Sturm bound: \(160\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(775, [\chi])\).

Total New Old
Modular forms 656 656 0
Cusp forms 624 624 0
Eisenstein series 32 32 0

Trace form

\( 624 q - 2 q^{2} - 12 q^{3} - 154 q^{4} - 3 q^{5} - 23 q^{6} - 34 q^{7} - 24 q^{8} + 62 q^{9} + O(q^{10}) \) \( 624 q - 2 q^{2} - 12 q^{3} - 154 q^{4} - 3 q^{5} - 23 q^{6} - 34 q^{7} - 24 q^{8} + 62 q^{9} - 14 q^{10} - 16 q^{11} + 6 q^{12} - 8 q^{13} - 5 q^{14} - 14 q^{15} - 150 q^{16} - 8 q^{17} - q^{18} - 8 q^{19} + 23 q^{20} + 17 q^{21} + 43 q^{22} - 24 q^{23} + 3 q^{24} + 47 q^{25} + 54 q^{26} - 12 q^{27} + 60 q^{28} - 116 q^{29} - 5 q^{30} - 16 q^{31} - 20 q^{32} - 54 q^{33} - 2 q^{34} + 23 q^{35} + 64 q^{36} - 17 q^{37} + 9 q^{38} - 24 q^{39} + 16 q^{40} + 13 q^{41} - 119 q^{42} - 26 q^{43} + 51 q^{44} - 36 q^{45} - 6 q^{46} - 57 q^{47} + 67 q^{48} - 72 q^{50} + 62 q^{51} + 37 q^{52} - 86 q^{53} + 46 q^{54} - 18 q^{55} + 59 q^{56} + 48 q^{57} - 86 q^{58} + 22 q^{59} + 96 q^{60} + 12 q^{61} + 7 q^{62} - 7 q^{63} - 160 q^{64} + 96 q^{65} - 212 q^{66} + 69 q^{67} + 13 q^{68} - 53 q^{69} - 75 q^{70} - 51 q^{71} - 51 q^{72} + 56 q^{73} - 78 q^{74} - 105 q^{75} + 104 q^{76} - 32 q^{77} - 69 q^{78} - 68 q^{79} + 33 q^{80} + 43 q^{81} - 56 q^{82} + 80 q^{83} + 21 q^{84} - 116 q^{85} - 62 q^{86} - 77 q^{87} - 133 q^{88} + 79 q^{89} - 179 q^{90} + q^{91} - 13 q^{92} + 174 q^{93} - 29 q^{94} + 5 q^{95} - 50 q^{96} + 49 q^{97} + 162 q^{98} + 199 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(775, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
775.2.bo.a 775.bo 775.ao $624$ $6.188$ None \(-2\) \(-12\) \(-3\) \(-34\) $\mathrm{SU}(2)[C_{15}]$