Properties

Label 8.14.b
Level 8
Weight 14
Character orbit b
Rep. character \(\chi_{8}(5,\cdot)\)
Character field \(\Q\)
Dimension 12
Newforms 2
Sturm bound 14
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 14 \)
Character orbit: \([\chi]\) = 8.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 8 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(14\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(8, [\chi])\).

Total New Old
Modular forms 14 14 0
Cusp forms 12 12 0
Eisenstein series 2 2 0

Trace form

\( 12q - 2q^{2} - 8556q^{4} + 58444q^{6} + 235296q^{7} + 1076872q^{8} - 5314412q^{9} + O(q^{10}) \) \( 12q - 2q^{2} - 8556q^{4} + 58444q^{6} + 235296q^{7} + 1076872q^{8} - 5314412q^{9} - 7752648q^{10} - 8536664q^{12} + 21101872q^{14} - 42373856q^{15} - 62847216q^{16} - 49714600q^{17} + 262778834q^{18} + 381237904q^{20} + 196775484q^{22} - 149850784q^{23} + 1739438480q^{24} - 1654349124q^{25} - 685452248q^{26} - 978617568q^{28} + 539961392q^{30} - 10881769344q^{31} - 8956909792q^{32} + 3397961328q^{33} + 8857451100q^{34} + 18075363660q^{36} - 23710846420q^{38} + 79057948000q^{39} - 6505554528q^{40} + 12231942520q^{41} - 3443304224q^{42} - 28647791928q^{44} - 51061300848q^{46} - 146392008000q^{47} - 161587694304q^{48} + 50764315692q^{49} + 246819442102q^{50} + 441779820720q^{52} - 639572716168q^{54} - 4023386208q^{55} - 699100837568q^{56} - 351867765712q^{57} + 992195908104q^{58} + 1614284565792q^{60} - 1019628353344q^{62} + 389587709920q^{63} - 1464077986752q^{64} + 173779028800q^{65} + 2946347707608q^{66} + 2850998874984q^{68} - 5505591528768q^{70} - 1892582134752q^{71} - 8538615449032q^{72} + 324055378296q^{73} + 9399657781240q^{74} + 10892359157736q^{76} - 16235130104944q^{78} + 4716009102144q^{79} - 16787669526720q^{80} + 410958020828q^{81} + 14910525285612q^{82} + 26784826987072q^{84} - 24718490913284q^{86} + 352970975712q^{87} - 26046521626416q^{88} + 5301429525304q^{89} + 43218339424520q^{90} + 34108342295904q^{92} - 37727942061792q^{94} - 15785048234464q^{95} - 62733552180160q^{96} - 10954301425896q^{97} + 61714328751438q^{98} + O(q^{100}) \)

Decomposition of \(S_{14}^{\mathrm{new}}(8, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
8.14.b.a \(2\) \(8.578\) \(\Q(\sqrt{-79}) \) None \(-112\) \(0\) \(0\) \(-351664\) \(q+(-56-4\beta )q^{2}+129\beta q^{3}+(-1920+\cdots)q^{4}+\cdots\)
8.14.b.b \(10\) \(8.578\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(110\) \(0\) \(0\) \(586960\) \(q+(11+\beta _{1})q^{2}+(3\beta _{1}+\beta _{3})q^{3}+(-472+\cdots)q^{4}+\cdots\)