Properties

Label 17.2
Level 17
Weight 2
Dimension 5
Nonzero newspaces 2
Newform subspaces 2
Sturm bound 48
Trace bound 1

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Defining parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 2 \)
Newform subspaces: \( 2 \)
Sturm bound: \(48\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(17))\).

Total New Old
Modular forms 20 20 0
Cusp forms 5 5 0
Eisenstein series 15 15 0

Trace form

\( 5q - 5q^{2} - 4q^{3} - q^{4} - 2q^{5} + 4q^{6} + 7q^{8} + 5q^{9} + O(q^{10}) \) \( 5q - 5q^{2} - 4q^{3} - q^{4} - 2q^{5} + 4q^{6} + 7q^{8} + 5q^{9} + 6q^{10} - 4q^{11} - 4q^{12} - 2q^{13} - 8q^{15} - 13q^{16} + q^{17} - 9q^{18} + 4q^{19} + 6q^{20} + 12q^{22} + 8q^{23} + 12q^{24} - 5q^{25} - 2q^{26} + 8q^{27} + 2q^{29} - 8q^{31} - q^{32} - 21q^{34} + 3q^{36} - 2q^{37} + 4q^{38} - 14q^{40} - 10q^{41} - 8q^{42} - 4q^{43} - 20q^{44} + 18q^{45} + 16q^{46} + 12q^{48} + 17q^{49} + 21q^{50} + 28q^{51} + 18q^{52} + 2q^{53} - 8q^{54} - 8q^{56} - 24q^{57} - 6q^{58} - 12q^{59} - 8q^{60} - 10q^{61} - 16q^{62} - 24q^{63} + 7q^{64} + 8q^{66} + 20q^{67} + 11q^{68} - 32q^{69} + 16q^{71} - 9q^{72} - 34q^{73} + 22q^{74} - 12q^{75} + 12q^{76} + 8q^{77} - 8q^{78} + 8q^{79} + 2q^{80} + 9q^{81} + 10q^{82} + 12q^{83} + 32q^{84} + 2q^{85} + 4q^{86} + 16q^{87} + 12q^{88} + 10q^{89} - 2q^{90} - 8q^{91} - 32q^{92} + 24q^{93} - 24q^{94} - 20q^{96} + 26q^{97} - 9q^{98} - 4q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
17.2.a \(\chi_{17}(1, \cdot)\) 17.2.a.a 1 1
17.2.b \(\chi_{17}(16, \cdot)\) None 0 1
17.2.c \(\chi_{17}(4, \cdot)\) None 0 2
17.2.d \(\chi_{17}(2, \cdot)\) 17.2.d.a 4 4

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T + 2 T^{2} \))(\( 1 + 4 T + 8 T^{2} + 12 T^{3} + 17 T^{4} + 24 T^{5} + 32 T^{6} + 32 T^{7} + 16 T^{8} \))
$3$ (\( 1 + 3 T^{2} \))(\( 1 + 4 T + 4 T^{2} - 12 T^{3} - 40 T^{4} - 36 T^{5} + 36 T^{6} + 108 T^{7} + 81 T^{8} \))
$5$ (\( 1 + 2 T + 5 T^{2} \))(\( 1 + 2 T^{2} - 16 T^{3} + 2 T^{4} - 80 T^{5} + 50 T^{6} + 625 T^{8} \))
$7$ (\( 1 - 4 T + 7 T^{2} \))(\( 1 + 4 T + 4 T^{2} - 28 T^{3} - 104 T^{4} - 196 T^{5} + 196 T^{6} + 1372 T^{7} + 2401 T^{8} \))
$11$ (\( 1 + 11 T^{2} \))(\( 1 + 4 T + 12 T^{2} + 60 T^{3} + 184 T^{4} + 660 T^{5} + 1452 T^{6} + 5324 T^{7} + 14641 T^{8} \))
$13$ (\( 1 + 2 T + 13 T^{2} \))(\( ( 1 - 24 T^{2} + 169 T^{4} )^{2} \))
$17$ (\( 1 - T \))(\( 1 + 2 T^{2} + 289 T^{4} \))
$19$ (\( 1 + 4 T + 19 T^{2} \))(\( 1 - 8 T + 32 T^{2} - 184 T^{3} + 1042 T^{4} - 3496 T^{5} + 11552 T^{6} - 54872 T^{7} + 130321 T^{8} \))
$23$ (\( 1 - 4 T + 23 T^{2} \))(\( 1 - 4 T + 12 T^{2} + 164 T^{3} - 712 T^{4} + 3772 T^{5} + 6348 T^{6} - 48668 T^{7} + 279841 T^{8} \))
$29$ (\( 1 - 6 T + 29 T^{2} \))(\( 1 + 4 T + 22 T^{2} + 244 T^{3} + 930 T^{4} + 7076 T^{5} + 18502 T^{6} + 97556 T^{7} + 707281 T^{8} \))
$31$ (\( 1 - 4 T + 31 T^{2} \))(\( 1 + 12 T + 108 T^{2} + 804 T^{3} + 5112 T^{4} + 24924 T^{5} + 103788 T^{6} + 357492 T^{7} + 923521 T^{8} \))
$37$ (\( 1 + 2 T + 37 T^{2} \))(\( 1 + 50 T^{2} - 240 T^{3} + 1250 T^{4} - 8880 T^{5} + 68450 T^{6} + 1874161 T^{8} \))
$41$ (\( 1 + 6 T + 41 T^{2} \))(\( ( 1 - 6 T + 41 T^{2} )^{2}( 1 + 16 T + 128 T^{2} + 656 T^{3} + 1681 T^{4} ) \))
$43$ (\( 1 - 4 T + 43 T^{2} \))(\( 1 + 8 T + 32 T^{2} + 376 T^{3} + 4402 T^{4} + 16168 T^{5} + 59168 T^{6} + 636056 T^{7} + 3418801 T^{8} \))
$47$ (\( 1 + 47 T^{2} \))(\( 1 - 44 T^{2} + 2854 T^{4} - 97196 T^{6} + 4879681 T^{8} \))
$53$ (\( 1 - 6 T + 53 T^{2} \))(\( ( 1 + 2 T + 2 T^{2} + 106 T^{3} + 2809 T^{4} )^{2} \))
$59$ (\( 1 + 12 T + 59 T^{2} \))(\( ( 1 - 20 T + 200 T^{2} - 1180 T^{3} + 3481 T^{4} )( 1 + 20 T + 200 T^{2} + 1180 T^{3} + 3481 T^{4} ) \))
$61$ (\( 1 + 10 T + 61 T^{2} \))(\( 1 + 50 T^{2} - 720 T^{3} + 1250 T^{4} - 43920 T^{5} + 186050 T^{6} + 13845841 T^{8} \))
$67$ (\( 1 - 4 T + 67 T^{2} \))(\( ( 1 - 8 T + 142 T^{2} - 536 T^{3} + 4489 T^{4} )^{2} \))
$71$ (\( 1 + 4 T + 71 T^{2} \))(\( 1 - 20 T + 100 T^{2} + 1420 T^{3} - 23400 T^{4} + 100820 T^{5} + 504100 T^{6} - 7158220 T^{7} + 25411681 T^{8} \))
$73$ (\( 1 + 6 T + 73 T^{2} \))(\( 1 + 28 T + 294 T^{2} + 1372 T^{3} + 4802 T^{4} + 100156 T^{5} + 1566726 T^{6} + 10892476 T^{7} + 28398241 T^{8} \))
$79$ (\( 1 - 12 T + 79 T^{2} \))(\( 1 + 4 T + 12 T^{2} - 836 T^{3} - 3400 T^{4} - 66044 T^{5} + 74892 T^{6} + 1972156 T^{7} + 38950081 T^{8} \))
$83$ (\( 1 + 4 T + 83 T^{2} \))(\( 1 - 16 T + 128 T^{2} - 1264 T^{3} + 12466 T^{4} - 104912 T^{5} + 881792 T^{6} - 9148592 T^{7} + 47458321 T^{8} \))
$89$ (\( 1 - 10 T + 89 T^{2} \))(\( 1 - 224 T^{2} + 27874 T^{4} - 1774304 T^{6} + 62742241 T^{8} \))
$97$ (\( 1 - 2 T + 97 T^{2} \))(\( 1 - 24 T + 242 T^{2} - 1704 T^{3} + 13730 T^{4} - 165288 T^{5} + 2276978 T^{6} - 21904152 T^{7} + 88529281 T^{8} \))
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