Properties

Label 76.5.l
Level $76$
Weight $5$
Character orbit 76.l
Rep. character $\chi_{76}(23,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $228$
Newform subspaces $1$
Sturm bound $50$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 76.l (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 76 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(50\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(76, [\chi])\).

Total New Old
Modular forms 252 252 0
Cusp forms 228 228 0
Eisenstein series 24 24 0

Trace form

\( 228 q - 6 q^{2} - 48 q^{4} - 12 q^{5} - 60 q^{6} - 3 q^{8} - 180 q^{9} + O(q^{10}) \) \( 228 q - 6 q^{2} - 48 q^{4} - 12 q^{5} - 60 q^{6} - 3 q^{8} - 180 q^{9} - 453 q^{10} - 3 q^{12} + 516 q^{13} + 81 q^{14} - 720 q^{16} - 12 q^{17} - 12 q^{18} - 1182 q^{20} - 930 q^{21} - 54 q^{22} - 2664 q^{24} - 12 q^{25} - 3099 q^{26} - 4824 q^{28} - 12 q^{29} + 5814 q^{30} + 7419 q^{32} + 1542 q^{33} + 6912 q^{34} + 8547 q^{36} - 24 q^{37} - 1536 q^{38} - 6942 q^{40} + 6396 q^{41} - 18855 q^{42} - 1143 q^{44} - 6 q^{45} - 1488 q^{46} + 6093 q^{48} + 26748 q^{49} + 8070 q^{50} - 12591 q^{52} + 2436 q^{53} - 7365 q^{54} - 14418 q^{56} - 12 q^{57} + 8268 q^{58} + 34632 q^{60} - 31068 q^{61} + 27396 q^{62} + 4575 q^{64} + 3594 q^{65} - 29556 q^{66} - 22782 q^{68} + 29370 q^{69} - 71541 q^{70} - 30174 q^{72} - 6348 q^{73} - 417 q^{74} + 43194 q^{76} - 50436 q^{77} + 45537 q^{78} + 30081 q^{80} - 41994 q^{81} + 72219 q^{82} + 13779 q^{84} - 59244 q^{85} + 19200 q^{86} - 22395 q^{88} + 1860 q^{89} + 45594 q^{90} - 64140 q^{92} + 59118 q^{93} - 55590 q^{94} - 98646 q^{96} - 5556 q^{97} - 52215 q^{98} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(76, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
76.5.l.a 76.l 76.l $228$ $7.856$ None \(-6\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{18}]$