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Properties

Label 775.2.bk
Level $775$
Weight $2$
Character orbit 775.bk
Rep. character $\chi_{775}(196,\cdot)$
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.bk (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

\( 624 q - 2 q^{2} + 3 q^{3} - 154 q^{4} - 3 q^{5} + 7 q^{6} - 34 q^{7} + 6 q^{8} - 293 q^{9} + O(q^{10}) \) \( 624 q - 2 q^{2} + 3 q^{3} - 154 q^{4} - 3 q^{5} + 7 q^{6} - 34 q^{7} + 6 q^{8} - 293 q^{9} - 4 q^{10} + 29 q^{11} - 4 q^{12} - 8 q^{13} + 15 q^{14} + q^{15} - 150 q^{16} - 8 q^{17} - q^{18} - 3 q^{19} - 12 q^{20} - 13 q^{21} + 53 q^{22} + q^{23} + 3 q^{24} - 13 q^{25} + 54 q^{26} - 102 q^{27} + 45 q^{28} + 14 q^{29} - 5 q^{30} - 6 q^{31} - 20 q^{32} + 6 q^{33} - 32 q^{34} + 48 q^{35} + 124 q^{36} + 28 q^{37} - 156 q^{38} + 16 q^{39} + 6 q^{40} - 2 q^{41} + 21 q^{42} - 26 q^{43} - 29 q^{44} + 29 q^{45} - 76 q^{46} + 18 q^{47} + 27 q^{48} - 27 q^{50} + 62 q^{51} + 97 q^{52} + 64 q^{53} + 6 q^{54} + 7 q^{55} + 29 q^{56} + 48 q^{57} + 104 q^{58} + 27 q^{59} + 51 q^{60} + 12 q^{61} - 48 q^{62} - 7 q^{63} - 130 q^{64} - 74 q^{65} - 32 q^{66} - 51 q^{67} + 13 q^{68} + 57 q^{69} + 5 q^{70} - 26 q^{71} - 181 q^{72} - 39 q^{73} - 78 q^{74} + 45 q^{75} + 104 q^{76} + 38 q^{77} - 114 q^{78} + 2 q^{79} + 53 q^{80} - 212 q^{81} - 56 q^{82} - 50 q^{83} + 91 q^{84} + 29 q^{85} + 53 q^{86} + 88 q^{87} + 107 q^{88} - 236 q^{89} + 71 q^{90} + 41 q^{91} - 13 q^{92} + 174 q^{93} - 29 q^{94} + 85 q^{95} + 60 q^{96} - 46 q^{97} - 168 q^{98} + 199 q^{99} + O(q^{100}) \)

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.bk.a 775.bk 775.ak $624$ $6.188$ None \(-2\) \(3\) \(-3\) \(-34\) $\mathrm{SU}(2)[C_{15}]$