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Properties

Label 3.17.b
Level 3
Weight 17
Character orbit b
Rep. character \(\chi_{3}(2,\cdot)\)
Character field \(\Q\)
Dimension 4
Newform subspaces 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3 \)
Weight: \( k \) = \( 17 \)
Character orbit: \([\chi]\) = 3.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{17}(3, [\chi])\).

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

Trace form

\( 4q - 2052q^{3} - 12464q^{4} - 403056q^{6} - 3141544q^{7} + 18618660q^{9} + O(q^{10}) \) \( 4q - 2052q^{3} - 12464q^{4} - 403056q^{6} - 3141544q^{7} + 18618660q^{9} - 18646560q^{10} + 572494608q^{12} - 1580730424q^{13} + 6829958880q^{15} - 14561268608q^{16} + 42304978080q^{18} - 56117116360q^{19} + 124455437064q^{21} - 173545812000q^{22} + 100515572352q^{24} - 8074048700q^{25} - 317983667652q^{27} + 746852001056q^{28} - 1762329117600q^{30} + 2471781156248q^{31} - 3610697951520q^{33} + 2721261612672q^{34} - 1219654126512q^{36} + 370563213896q^{37} + 7022170227384q^{39} - 11795287092480q^{40} + 27587883687840q^{42} - 28065022062664q^{43} + 18795326443200q^{45} - 43994579504832q^{46} + 41041959355008q^{48} + 29478262537164q^{49} - 82841575222656q^{51} + 42193089120416q^{52} - 107063660756304q^{54} + 290253653236800q^{55} - 335129108488344q^{57} + 8796421982880q^{58} + 56126440892160q^{60} + 362269793083208q^{61} - 266698363786344q^{63} - 653949742779392q^{64} + 1332768950045280q^{66} - 26774405363464q^{67} + 58823173290816q^{69} - 2292362286177600q^{70} + 2397649754476800q^{72} + 317628887539976q^{73} - 1511365865026500q^{75} - 2008642200508384q^{76} + 1538179445855520q^{78} + 4794017165184920q^{79} - 6444192852054396q^{81} + 1589112481320000q^{82} - 1210523902199136q^{84} + 7999994092573440q^{85} - 8850169595242080q^{87} - 3370289894104320q^{88} + 3549134645307360q^{90} + 9328538231657008q^{91} - 2064207396761784q^{93} - 12859596129667968q^{94} + 15507630559798272q^{96} - 13833795002601784q^{97} + 18943177097338560q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{17}^{\mathrm{new}}(3, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
3.17.b.a \(4\) \(4.870\) \(\mathbb{Q}[x]/(x^{4} + \cdots)\) None \(0\) \(-2052\) \(0\) \(-3141544\) \(q+\beta _{1}q^{2}+(-513+\beta _{1}+\beta _{2})q^{3}+(-3116+\cdots)q^{4}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 - 124840 T^{2} + 11637040128 T^{4} - 536183717232640 T^{6} + 18446744073709551616 T^{8} \)
$3$ \( 1 + 2052 T - 7203978 T^{2} + 88331871492 T^{3} + 1853020188851841 T^{4} \)
$5$ \( 1 - 301138756900 T^{2} + \)\(63\!\cdots\!50\)\( T^{4} - \)\(70\!\cdots\!00\)\( T^{6} + \)\(54\!\cdots\!25\)\( T^{8} \)
$7$ \( ( 1 + 1570772 T + 27097027273302 T^{2} + 52201356816673301972 T^{3} + \)\(11\!\cdots\!01\)\( T^{4} )^{2} \)
$11$ \( 1 - 55051819252795684 T^{2} + \)\(21\!\cdots\!06\)\( T^{4} - \)\(11\!\cdots\!64\)\( T^{6} + \)\(44\!\cdots\!41\)\( T^{8} \)
$13$ \( ( 1 + 790365212 T + 1384777667105257542 T^{2} + \)\(52\!\cdots\!92\)\( T^{3} + \)\(44\!\cdots\!81\)\( T^{4} )^{2} \)
$17$ \( 1 - \)\(13\!\cdots\!60\)\( T^{2} + \)\(81\!\cdots\!58\)\( T^{4} - \)\(31\!\cdots\!60\)\( T^{6} + \)\(56\!\cdots\!21\)\( T^{8} \)
$19$ \( ( 1 + 28058558180 T + \)\(42\!\cdots\!98\)\( T^{2} + \)\(80\!\cdots\!80\)\( T^{3} + \)\(83\!\cdots\!61\)\( T^{4} )^{2} \)
$23$ \( 1 - \)\(20\!\cdots\!40\)\( T^{2} + \)\(18\!\cdots\!78\)\( T^{4} - \)\(78\!\cdots\!40\)\( T^{6} + \)\(14\!\cdots\!41\)\( T^{8} \)
$29$ \( 1 - \)\(48\!\cdots\!44\)\( T^{2} + \)\(17\!\cdots\!66\)\( T^{4} - \)\(30\!\cdots\!04\)\( T^{6} + \)\(39\!\cdots\!81\)\( T^{8} \)
$31$ \( ( 1 - 1235890578124 T + \)\(18\!\cdots\!06\)\( T^{2} - \)\(89\!\cdots\!44\)\( T^{3} + \)\(52\!\cdots\!61\)\( T^{4} )^{2} \)
$37$ \( ( 1 - 185281606948 T + \)\(24\!\cdots\!22\)\( T^{2} - \)\(22\!\cdots\!68\)\( T^{3} + \)\(15\!\cdots\!81\)\( T^{4} )^{2} \)
$41$ \( 1 - \)\(23\!\cdots\!04\)\( T^{2} + \)\(21\!\cdots\!66\)\( T^{4} - \)\(94\!\cdots\!24\)\( T^{6} + \)\(16\!\cdots\!61\)\( T^{8} \)
$43$ \( ( 1 + 14032511031332 T + \)\(22\!\cdots\!02\)\( T^{2} + \)\(19\!\cdots\!32\)\( T^{3} + \)\(18\!\cdots\!01\)\( T^{4} )^{2} \)
$47$ \( 1 - \)\(18\!\cdots\!60\)\( T^{2} + \)\(14\!\cdots\!98\)\( T^{4} - \)\(59\!\cdots\!60\)\( T^{6} + \)\(10\!\cdots\!81\)\( T^{8} \)
$53$ \( 1 - \)\(12\!\cdots\!60\)\( T^{2} + \)\(71\!\cdots\!98\)\( T^{4} - \)\(19\!\cdots\!60\)\( T^{6} + \)\(22\!\cdots\!81\)\( T^{8} \)
$59$ \( 1 - \)\(16\!\cdots\!04\)\( T^{2} + \)\(93\!\cdots\!66\)\( T^{4} - \)\(77\!\cdots\!24\)\( T^{6} + \)\(21\!\cdots\!61\)\( T^{8} \)
$61$ \( ( 1 - 181134896541604 T + \)\(81\!\cdots\!26\)\( T^{2} - \)\(66\!\cdots\!44\)\( T^{3} + \)\(13\!\cdots\!21\)\( T^{4} )^{2} \)
$67$ \( ( 1 + 13387202681732 T + \)\(30\!\cdots\!42\)\( T^{2} + \)\(22\!\cdots\!92\)\( T^{3} + \)\(27\!\cdots\!61\)\( T^{4} )^{2} \)
$71$ \( 1 - \)\(12\!\cdots\!44\)\( T^{2} + \)\(66\!\cdots\!66\)\( T^{4} - \)\(21\!\cdots\!04\)\( T^{6} + \)\(30\!\cdots\!81\)\( T^{8} \)
$73$ \( ( 1 - 158814443769988 T + \)\(37\!\cdots\!62\)\( T^{2} - \)\(10\!\cdots\!68\)\( T^{3} + \)\(42\!\cdots\!21\)\( T^{4} )^{2} \)
$79$ \( ( 1 - 2397008582592460 T + \)\(47\!\cdots\!38\)\( T^{2} - \)\(55\!\cdots\!60\)\( T^{3} + \)\(52\!\cdots\!41\)\( T^{4} )^{2} \)
$83$ \( 1 - \)\(46\!\cdots\!60\)\( T^{2} - \)\(18\!\cdots\!42\)\( T^{4} - \)\(12\!\cdots\!60\)\( T^{6} + \)\(66\!\cdots\!21\)\( T^{8} \)
$89$ \( 1 - \)\(45\!\cdots\!84\)\( T^{2} + \)\(22\!\cdots\!06\)\( T^{4} - \)\(10\!\cdots\!64\)\( T^{6} + \)\(57\!\cdots\!41\)\( T^{8} \)
$97$ \( ( 1 + 6916897501300892 T + \)\(13\!\cdots\!62\)\( T^{2} + \)\(42\!\cdots\!32\)\( T^{3} + \)\(37\!\cdots\!41\)\( T^{4} )^{2} \)
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