Properties

Label 17.4.b
Level 17
Weight 4
Character orbit b
Rep. character \(\chi_{17}(16,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 17 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 17.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 17 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(17, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 4 4 0
Eisenstein series 2 2 0

Trace form

\( 4q - 2q^{2} + 2q^{4} - 18q^{8} - 40q^{9} + O(q^{10}) \) \( 4q - 2q^{2} + 2q^{4} - 18q^{8} - 40q^{9} + 140q^{13} + 24q^{15} - 238q^{16} + 112q^{17} + 218q^{18} - 112q^{19} + 124q^{21} - 460q^{25} - 532q^{26} + 912q^{30} + 494q^{32} - 1036q^{33} + 406q^{34} + 936q^{35} - 218q^{36} + 56q^{38} - 1184q^{42} - 520q^{43} + 952q^{47} + 312q^{49} - 1354q^{50} + 1160q^{51} + 532q^{52} - 576q^{53} + 168q^{55} - 1176q^{59} - 912q^{60} + 1426q^{64} + 1904q^{66} - 240q^{67} - 406q^{68} + 1204q^{69} + 192q^{70} - 1206q^{72} - 56q^{76} + 868q^{77} - 2408q^{81} - 2856q^{83} + 1184q^{84} + 768q^{85} - 2248q^{86} - 168q^{87} + 1988q^{89} + 1060q^{93} + 448q^{94} + 306q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(17, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
17.4.b.a \(4\) \(1.003\) 4.0.4669632.2 None \(-2\) \(0\) \(0\) \(0\) \(q+(-1+\beta _{2})q^{2}+\beta _{1}q^{3}+(1-\beta _{2})q^{4}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( ( 1 + T + 8 T^{2} + 8 T^{3} + 64 T^{4} )^{2} \)
$3$ \( 1 - 34 T^{2} + 1450 T^{4} - 24786 T^{6} + 531441 T^{8} \)
$5$ \( 1 - 20 T^{2} + 12342 T^{4} - 312500 T^{6} + 244140625 T^{8} \)
$7$ \( 1 - 842 T^{2} + 410922 T^{4} - 99060458 T^{6} + 13841287201 T^{8} \)
$11$ \( 1 - 1698 T^{2} + 3550826 T^{4} - 3008110578 T^{6} + 3138428376721 T^{8} \)
$13$ \( ( 1 - 70 T + 4002 T^{2} - 153790 T^{3} + 4826809 T^{4} )^{2} \)
$17$ \( 1 - 112 T + 6494 T^{2} - 550256 T^{3} + 24137569 T^{4} \)
$19$ \( ( 1 + 28 T + 6859 T^{2} )^{4} \)
$23$ \( 1 - 20346 T^{2} + 209323274 T^{4} - 3011938197594 T^{6} + 21914624432020321 T^{8} \)
$29$ \( 1 - 74036 T^{2} + 2514340758 T^{4} - 44038339393556 T^{6} + 353814783205469041 T^{8} \)
$31$ \( 1 - 114890 T^{2} + 5074759530 T^{4} - 101965297910090 T^{6} + 787662783788549761 T^{8} \)
$37$ \( 1 - 116372 T^{2} + 7903483062 T^{4} - 298578713668148 T^{6} + 6582952005840035281 T^{8} \)
$41$ \( 1 - 158724 T^{2} + 15178105958 T^{4} - 753955545548484 T^{6} + 22563490300366186081 T^{8} \)
$43$ \( ( 1 + 260 T + 128262 T^{2} + 20671820 T^{3} + 6321363049 T^{4} )^{2} \)
$47$ \( ( 1 - 476 T + 257822 T^{2} - 49419748 T^{3} + 10779215329 T^{4} )^{2} \)
$53$ \( ( 1 + 288 T + 248662 T^{2} + 42876576 T^{3} + 22164361129 T^{4} )^{2} \)
$59$ \( ( 1 + 588 T + 335494 T^{2} + 120762852 T^{3} + 42180533641 T^{4} )^{2} \)
$61$ \( 1 - 425396 T^{2} + 97219598358 T^{4} - 21916561171671956 T^{6} + \)\(26\!\cdots\!21\)\( T^{8} \)
$67$ \( ( 1 + 120 T + 571334 T^{2} + 36091560 T^{3} + 90458382169 T^{4} )^{2} \)
$71$ \( 1 - 1379018 T^{2} + 731023514346 T^{4} - 176652597332169578 T^{6} + \)\(16\!\cdots\!41\)\( T^{8} \)
$73$ \( 1 + 55196 T^{2} + 301853502630 T^{4} + 8353043954247644 T^{6} + \)\(22\!\cdots\!21\)\( T^{8} \)
$79$ \( 1 - 1282922 T^{2} + 849811865706 T^{4} - 311862244611912362 T^{6} + \)\(59\!\cdots\!41\)\( T^{8} \)
$83$ \( ( 1 + 1428 T + 1595158 T^{2} + 816511836 T^{3} + 326940373369 T^{4} )^{2} \)
$89$ \( ( 1 - 994 T + 1642394 T^{2} - 700739186 T^{3} + 496981290961 T^{4} )^{2} \)
$97$ \( 1 - 3375140 T^{2} + 4511732954310 T^{4} - 2811397132716065060 T^{6} + \)\(69\!\cdots\!41\)\( T^{8} \)
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