Properties

Label 17.2.d
Level 17
Weight 2
Character orbit d
Rep. character \(\chi_{17}(2,\cdot)\)
Character field \(\Q(\zeta_{8})\)
Dimension 4
Newform subspaces 1
Sturm bound 3
Trace bound 0

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Defining parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 17.d (of order \(8\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 17 \)
Character field: \(\Q(\zeta_{8})\)
Newform subspaces: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(17, [\chi])\).

Total New Old
Modular forms 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

Trace form

\( 4q - 4q^{2} - 4q^{3} + 4q^{6} - 4q^{7} + 4q^{8} + 8q^{9} + O(q^{10}) \) \( 4q - 4q^{2} - 4q^{3} + 4q^{6} - 4q^{7} + 4q^{8} + 8q^{9} + 4q^{10} - 4q^{11} - 4q^{12} + 4q^{14} - 8q^{15} - 12q^{16} - 12q^{18} + 8q^{19} + 4q^{20} + 12q^{22} + 4q^{23} + 12q^{24} - 4q^{25} - 4q^{26} + 8q^{27} + 4q^{28} - 4q^{29} - 12q^{31} + 4q^{32} - 20q^{34} + 8q^{35} - 8q^{40} - 4q^{41} - 8q^{42} - 8q^{43} - 20q^{44} + 12q^{45} + 20q^{46} + 12q^{48} + 8q^{49} + 20q^{50} + 28q^{51} + 16q^{52} - 4q^{53} - 8q^{54} - 20q^{56} - 24q^{57} - 8q^{60} - 12q^{62} - 12q^{63} - 4q^{65} + 8q^{66} + 16q^{67} + 12q^{68} - 32q^{69} - 8q^{70} + 20q^{71} - 28q^{73} + 20q^{74} - 12q^{75} + 8q^{76} + 8q^{77} - 8q^{78} - 4q^{79} + 4q^{82} + 16q^{83} + 32q^{84} + 4q^{85} + 8q^{86} + 16q^{87} + 12q^{88} + 4q^{90} - 28q^{92} + 24q^{93} - 24q^{94} - 8q^{95} - 20q^{96} + 24q^{97} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(17, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
17.2.d.a \(4\) \(0.136\) \(\Q(\zeta_{8})\) None \(-4\) \(-4\) \(0\) \(-4\) \(q+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{2}+(-1-\zeta_{8}+\cdots)q^{3}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + 4 T + 8 T^{2} + 12 T^{3} + 17 T^{4} + 24 T^{5} + 32 T^{6} + 32 T^{7} + 16 T^{8} \)
$3$ \( 1 + 4 T + 4 T^{2} - 12 T^{3} - 40 T^{4} - 36 T^{5} + 36 T^{6} + 108 T^{7} + 81 T^{8} \)
$5$ \( 1 + 2 T^{2} - 16 T^{3} + 2 T^{4} - 80 T^{5} + 50 T^{6} + 625 T^{8} \)
$7$ \( 1 + 4 T + 4 T^{2} - 28 T^{3} - 104 T^{4} - 196 T^{5} + 196 T^{6} + 1372 T^{7} + 2401 T^{8} \)
$11$ \( 1 + 4 T + 12 T^{2} + 60 T^{3} + 184 T^{4} + 660 T^{5} + 1452 T^{6} + 5324 T^{7} + 14641 T^{8} \)
$13$ \( ( 1 - 24 T^{2} + 169 T^{4} )^{2} \)
$17$ \( 1 + 2 T^{2} + 289 T^{4} \)
$19$ \( 1 - 8 T + 32 T^{2} - 184 T^{3} + 1042 T^{4} - 3496 T^{5} + 11552 T^{6} - 54872 T^{7} + 130321 T^{8} \)
$23$ \( 1 - 4 T + 12 T^{2} + 164 T^{3} - 712 T^{4} + 3772 T^{5} + 6348 T^{6} - 48668 T^{7} + 279841 T^{8} \)
$29$ \( 1 + 4 T + 22 T^{2} + 244 T^{3} + 930 T^{4} + 7076 T^{5} + 18502 T^{6} + 97556 T^{7} + 707281 T^{8} \)
$31$ \( 1 + 12 T + 108 T^{2} + 804 T^{3} + 5112 T^{4} + 24924 T^{5} + 103788 T^{6} + 357492 T^{7} + 923521 T^{8} \)
$37$ \( 1 + 50 T^{2} - 240 T^{3} + 1250 T^{4} - 8880 T^{5} + 68450 T^{6} + 1874161 T^{8} \)
$41$ \( ( 1 - 6 T + 41 T^{2} )^{2}( 1 + 16 T + 128 T^{2} + 656 T^{3} + 1681 T^{4} ) \)
$43$ \( 1 + 8 T + 32 T^{2} + 376 T^{3} + 4402 T^{4} + 16168 T^{5} + 59168 T^{6} + 636056 T^{7} + 3418801 T^{8} \)
$47$ \( 1 - 44 T^{2} + 2854 T^{4} - 97196 T^{6} + 4879681 T^{8} \)
$53$ \( ( 1 + 2 T + 2 T^{2} + 106 T^{3} + 2809 T^{4} )^{2} \)
$59$ \( ( 1 - 20 T + 200 T^{2} - 1180 T^{3} + 3481 T^{4} )( 1 + 20 T + 200 T^{2} + 1180 T^{3} + 3481 T^{4} ) \)
$61$ \( 1 + 50 T^{2} - 720 T^{3} + 1250 T^{4} - 43920 T^{5} + 186050 T^{6} + 13845841 T^{8} \)
$67$ \( ( 1 - 8 T + 142 T^{2} - 536 T^{3} + 4489 T^{4} )^{2} \)
$71$ \( 1 - 20 T + 100 T^{2} + 1420 T^{3} - 23400 T^{4} + 100820 T^{5} + 504100 T^{6} - 7158220 T^{7} + 25411681 T^{8} \)
$73$ \( 1 + 28 T + 294 T^{2} + 1372 T^{3} + 4802 T^{4} + 100156 T^{5} + 1566726 T^{6} + 10892476 T^{7} + 28398241 T^{8} \)
$79$ \( 1 + 4 T + 12 T^{2} - 836 T^{3} - 3400 T^{4} - 66044 T^{5} + 74892 T^{6} + 1972156 T^{7} + 38950081 T^{8} \)
$83$ \( 1 - 16 T + 128 T^{2} - 1264 T^{3} + 12466 T^{4} - 104912 T^{5} + 881792 T^{6} - 9148592 T^{7} + 47458321 T^{8} \)
$89$ \( 1 - 224 T^{2} + 27874 T^{4} - 1774304 T^{6} + 62742241 T^{8} \)
$97$ \( 1 - 24 T + 242 T^{2} - 1704 T^{3} + 13730 T^{4} - 165288 T^{5} + 2276978 T^{6} - 21904152 T^{7} + 88529281 T^{8} \)
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