Properties

Label 731.2.bd
Level $731$
Weight $2$
Character orbit 731.bd
Rep. character $\chi_{731}(7,\cdot)$
Character field $\Q(\zeta_{48})$
Dimension $1024$
Newform subspaces $1$
Sturm bound $132$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 731 = 17 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 731.bd (of order \(48\) and degree \(16\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 731 \)
Character field: \(\Q(\zeta_{48})\)
Newform subspaces: \( 1 \)
Sturm bound: \(132\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(731, [\chi])\).

Total New Old
Modular forms 1088 1088 0
Cusp forms 1024 1024 0
Eisenstein series 64 64 0

Trace form

\( 1024 q - 24 q^{3} - 32 q^{4} - 24 q^{5} - 8 q^{6} - 24 q^{7} - 8 q^{9} + O(q^{10}) \) \( 1024 q - 24 q^{3} - 32 q^{4} - 24 q^{5} - 8 q^{6} - 24 q^{7} - 8 q^{9} - 8 q^{10} - 48 q^{11} - 24 q^{12} - 16 q^{13} - 8 q^{14} - 8 q^{15} - 8 q^{17} - 48 q^{18} - 24 q^{19} - 24 q^{20} - 32 q^{21} + 40 q^{24} - 24 q^{25} - 24 q^{26} - 24 q^{28} - 24 q^{29} - 24 q^{30} + 24 q^{31} - 24 q^{34} - 192 q^{35} + 8 q^{36} - 24 q^{37} - 16 q^{38} - 8 q^{40} - 32 q^{41} + 24 q^{43} + 32 q^{44} + 72 q^{46} + 48 q^{47} + 48 q^{48} - 8 q^{49} - 144 q^{52} - 8 q^{53} + 144 q^{54} + 72 q^{55} - 8 q^{56} - 24 q^{57} - 128 q^{58} + 96 q^{59} - 112 q^{60} + 24 q^{61} - 192 q^{62} - 24 q^{63} + 192 q^{64} - 136 q^{66} - 8 q^{68} - 96 q^{69} - 24 q^{71} - 432 q^{72} - 24 q^{73} + 88 q^{74} + 144 q^{76} - 24 q^{77} - 496 q^{78} - 40 q^{79} + 264 q^{80} - 120 q^{81} - 16 q^{83} - 48 q^{86} - 32 q^{87} - 24 q^{89} - 112 q^{90} - 24 q^{91} + 184 q^{92} + 168 q^{93} + 72 q^{95} + 40 q^{96} - 160 q^{97} - 432 q^{98} + 8 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(731, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
731.2.bd.a 731.bd 731.ad $1024$ $5.837$ None \(0\) \(-24\) \(-24\) \(-24\) $\mathrm{SU}(2)[C_{48}]$