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

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

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 \(110\) \(0\) \(0\) \(586960\) \(q+(11+\beta _{1})q^{2}+(3\beta _{1}+\beta _{3})q^{3}+(-472+\cdots)q^{4}+\cdots\)