Properties

Label 8.17.d
Level 8
Weight 17
Character orbit d
Rep. character \(\chi_{8}(3,\cdot)\)
Character field \(\Q\)
Dimension 15
Newforms 2
Sturm bound 17
Trace bound 1

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Defining parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 17 \)
Character orbit: \([\chi]\) = 8.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 8 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(17\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(8, [\chi])\).

Total New Old
Modular forms 17 17 0
Cusp forms 15 15 0
Eisenstein series 2 2 0

Trace form

\( 15q - 94q^{2} - 2q^{3} + 11316q^{4} + 1804828q^{6} + 27676376q^{8} + 186535789q^{9} + O(q^{10}) \) \( 15q - 94q^{2} - 2q^{3} + 11316q^{4} + 1804828q^{6} + 27676376q^{8} + 186535789q^{9} + 87155280q^{10} + 260133502q^{11} - 752587592q^{12} - 2675193504q^{14} + 14011341840q^{16} + 2448153118q^{17} + 17943353254q^{18} + 34180272894q^{19} + 31953450720q^{20} + 27681042588q^{22} - 145793747312q^{24} - 277318741425q^{25} - 518273679696q^{26} - 27222843140q^{27} + 102542376000q^{28} - 364331826720q^{30} + 1195262708576q^{32} + 333517318460q^{33} + 4198740617988q^{34} - 3057653406720q^{35} - 3006616968932q^{36} + 1652467209628q^{38} - 4027933291200q^{40} + 9551628802462q^{41} - 6653698130880q^{42} + 22785747288702q^{43} + 15916637387704q^{44} + 21043605267744q^{46} - 4831276690592q^{48} - 71507840830833q^{49} - 15421196687710q^{50} - 107865445804036q^{51} - 73249356722400q^{52} - 192920217281096q^{54} + 110873799752064q^{56} + 33194571799100q^{57} + 256627273576560q^{58} + 637925910858622q^{59} - 83822619107520q^{60} + 346701622780800q^{62} - 50698612807104q^{64} + 220877370432000q^{65} - 71491343932216q^{66} - 1231951009031682q^{67} - 420959812997912q^{68} - 442172390987520q^{70} + 367812042286984q^{72} - 1029028020615522q^{73} + 2394643836493776q^{74} + 1036118873764990q^{75} - 2498418556586568q^{76} - 4928152344599520q^{78} + 6402194304908160q^{80} - 1480249668662069q^{81} + 5023711994128068q^{82} + 3770478787150078q^{83} - 9316784627856000q^{84} - 7409416172984804q^{86} + 8585657603395728q^{88} + 842724399508894q^{89} + 14680290550241520q^{90} - 7162887702930432q^{91} - 9213856910218560q^{92} - 15838781433150144q^{94} + 35760948162215488q^{96} + 8690853020527902q^{97} + 42513201019111586q^{98} + 12035501702203898q^{99} + O(q^{100}) \)

Decomposition of \(S_{17}^{\mathrm{new}}(8, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
8.17.d.a \(1\) \(12.986\) \(\Q\) \(\Q(\sqrt{-2}) \) \(256\) \(-11966\) \(0\) \(0\) \(q+2^{8}q^{2}-11966q^{3}+2^{16}q^{4}-3063296q^{6}+\cdots\)
8.17.d.b \(14\) \(12.986\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-350\) \(11964\) \(0\) \(0\) \(q+(-5^{2}-\beta _{1})q^{2}+(855-6\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)