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Properties

Label 8.17.d
Level $8$
Weight $17$
Character orbit 8.d
Rep. character $\chi_{8}(3,\cdot)$
Character field $\Q$
Dimension $15$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{17}^{\mathrm{new}}(8, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
8.17.d.a 8.d 8.d $1$ $12.986$ \(\Q\) \(\Q(\sqrt{-2}) \) \(256\) \(-11966\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2^{8}q^{2}-11966q^{3}+2^{16}q^{4}-3063296q^{6}+\cdots\)
8.17.d.b 8.d 8.d $14$ $12.986$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-350\) \(11964\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-5^{2}-\beta _{1})q^{2}+(855-6\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)