↑

Properties

Label 775.2.bn
Level $775$
Weight $2$
Character orbit 775.bn
Rep. character $\chi_{775}(41,\cdot)$
Character field $\Q(\zeta_{15})$
Dimension $624$
Newform subspaces $1$
Sturm bound $160$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 775.bn (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

\( 624 q - 2 q^{2} - 7 q^{3} - 154 q^{4} - 3 q^{5} + 7 q^{6} - 14 q^{7} + 26 q^{8} + 67 q^{9} + O(q^{10}) \) \( 624 q - 2 q^{2} - 7 q^{3} - 154 q^{4} - 3 q^{5} + 7 q^{6} - 14 q^{7} + 26 q^{8} + 67 q^{9} - 4 q^{10} - 16 q^{11} - 9 q^{12} - 8 q^{13} - 10 q^{14} - 34 q^{15} - 130 q^{16} - 8 q^{17} - 46 q^{18} - 8 q^{19} - 27 q^{20} - 28 q^{21} - 2 q^{22} - 9 q^{23} - 92 q^{24} - 13 q^{25} + 19 q^{26} + 23 q^{27} - 50 q^{28} + 34 q^{29} - 60 q^{30} - 16 q^{31} + 10 q^{32} + 41 q^{33} - 12 q^{34} + 13 q^{35} + 34 q^{36} - 17 q^{37} + 99 q^{38} - 14 q^{39} - 9 q^{40} + 3 q^{41} + 81 q^{42} + 4 q^{43} - 34 q^{44} + 14 q^{45} + 34 q^{46} - 2 q^{47} + 52 q^{48} + 60 q^{49} + 28 q^{50} - 43 q^{51} + 77 q^{52} - 21 q^{53} - 184 q^{54} - 33 q^{55} + 124 q^{56} - 52 q^{57} - 56 q^{58} + 12 q^{59} - 79 q^{60} + 12 q^{61} + 17 q^{62} - 72 q^{63} - 90 q^{64} - 9 q^{65} + 8 q^{66} - q^{67} - 32 q^{68} + 32 q^{69} - 60 q^{70} + 19 q^{71} - 101 q^{72} - 4 q^{73} - 43 q^{74} - 10 q^{75} - 86 q^{76} - 52 q^{77} - 59 q^{78} + 127 q^{79} + 18 q^{80} + 83 q^{81} + 29 q^{82} - 50 q^{83} - 39 q^{84} + 59 q^{85} - 52 q^{86} + 3 q^{87} + 22 q^{88} + 64 q^{89} - 84 q^{90} - 204 q^{91} - 78 q^{92} + 34 q^{93} - 29 q^{94} - 80 q^{95} + 30 q^{96} - 31 q^{97} + 27 q^{98} - 16 q^{99} + O(q^{100}) \)

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.bn.a 775.bn 775.an $624$ $6.188$ None \(-2\) \(-7\) \(-3\) \(-14\) $\mathrm{SU}(2)[C_{15}]$