Properties

Label 775.2.bx
Level $775$
Weight $2$
Character orbit 775.bx
Rep. character $\chi_{775}(23,\cdot)$
Character field $\Q(\zeta_{20})$
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.bx (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 775 \)
Character field: \(\Q(\zeta_{20})\)
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

\( 624 q - 6 q^{2} - 20 q^{3} - 10 q^{4} - 16 q^{5} - 18 q^{7} - 20 q^{8} + O(q^{10}) \) \( 624 q - 6 q^{2} - 20 q^{3} - 10 q^{4} - 16 q^{5} - 18 q^{7} - 20 q^{8} + 6 q^{10} - 60 q^{12} - 10 q^{13} - 40 q^{14} - 70 q^{15} + 142 q^{16} - 10 q^{17} - 6 q^{18} - 18 q^{20} - 10 q^{21} - 10 q^{22} - 10 q^{23} - 4 q^{25} + 10 q^{27} - 78 q^{28} - 10 q^{29} + 160 q^{30} - 6 q^{31} - 16 q^{32} - 6 q^{33} - 10 q^{34} - 72 q^{35} + 132 q^{36} + 40 q^{37} - 62 q^{38} - 10 q^{39} - 14 q^{40} - 2 q^{41} - 10 q^{42} - 10 q^{43} - 80 q^{44} + 42 q^{45} - 24 q^{47} - 10 q^{48} - 60 q^{49} - 134 q^{50} - 12 q^{51} - 120 q^{52} + 90 q^{53} + 50 q^{54} + 80 q^{55} - 4 q^{56} + 80 q^{57} + 70 q^{58} - 40 q^{59} - 150 q^{60} - 74 q^{62} + 40 q^{63} + 30 q^{64} + 40 q^{65} + 10 q^{66} + 32 q^{67} - 180 q^{68} - 10 q^{69} - 20 q^{70} - 42 q^{71} + 302 q^{72} + 30 q^{73} - 10 q^{75} - 4 q^{76} + 50 q^{77} - 24 q^{78} - 110 q^{79} - 8 q^{80} - 568 q^{81} - 44 q^{82} + 100 q^{83} - 20 q^{84} - 10 q^{85} - 130 q^{87} + 100 q^{88} - 20 q^{89} + 18 q^{90} - 10 q^{91} - 70 q^{92} - 170 q^{93} + 50 q^{94} + 144 q^{95} + 122 q^{97} - 66 q^{98} + 180 q^{99} + O(q^{100}) \)

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.bx.a 775.bx 775.ax $624$ $6.188$ None \(-6\) \(-20\) \(-16\) \(-18\) $\mathrm{SU}(2)[C_{20}]$