Properties

Label 3.11
Level 3
Weight 11
Dimension 2
Nonzero newspaces 1
Newform subspaces 1
Sturm bound 7
Trace bound 0

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Defining parameters

Level: \( N \) = \( 3\( 3 \) \)
Weight: \( k \) = \( 11 \)
Nonzero newspaces: \( 1 \)
Newform subspaces: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(\Gamma_1(3))\).

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

Trace form

\( 2q - 54q^{3} + 608q^{4} - 12960q^{6} + 34468q^{7} - 115182q^{9} + O(q^{10}) \) \( 2q - 54q^{3} + 608q^{4} - 12960q^{6} + 34468q^{7} - 115182q^{9} + 152640q^{10} - 16416q^{12} - 339308q^{13} + 1373760q^{15} - 1289728q^{16} + 699840q^{18} - 1898924q^{19} - 930636q^{21} + 10025280q^{22} - 17210880q^{24} + 3351410q^{25} + 9408474q^{27} + 10478272q^{28} - 4121280q^{30} - 59586236q^{31} + 90227520q^{33} + 18420480q^{34} - 35015328q^{36} - 121623692q^{37} + 9161316q^{39} + 202705920q^{40} - 223352640q^{42} + 214839412q^{43} - 74183040q^{45} - 142623360q^{46} + 34822656q^{48} + 29071014q^{49} + 165784320q^{51} - 103149632q^{52} + 727483680q^{54} - 1062679680q^{55} + 51270948q^{57} - 170775360q^{58} + 417623040q^{60} + 2061587284q^{61} - 1985046588q^{63} - 2350292992q^{64} - 270682560q^{66} + 3753484948q^{67} - 1283610240q^{69} + 2630597760q^{70} + 929387520q^{72} - 5693056988q^{73} - 90488070q^{75} - 577272896q^{76} + 2198715840q^{78} + 2977295236q^{79} + 6293324322q^{81} - 9749335680q^{82} - 282913344q^{84} - 1952570880q^{85} - 1536978240q^{87} + 13313571840q^{88} - 8790690240q^{90} - 5847634072q^{91} + 1608828372q^{93} + 14382155520q^{94} - 9266503680q^{96} - 3185897852q^{97} - 4872286080q^{99} + O(q^{100}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(\Gamma_1(3))\)

We only show spaces with odd 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
3.11.b \(\chi_{3}(2, \cdot)\) 3.11.b.a 2 1

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 1328 T^{2} + 1048576 T^{4} \)
$3$ \( 1 + 54 T + 59049 T^{2} \)
$5$ \( 1 - 11441330 T^{2} + 95367431640625 T^{4} \)
$7$ \( ( 1 - 17234 T + 282475249 T^{2} )^{2} \)
$11$ \( 1 - 16976849522 T^{2} + \)\(67\!\cdots\!01\)\( T^{4} \)
$13$ \( ( 1 + 169654 T + 137858491849 T^{2} )^{2} \)
$17$ \( 1 - 3914170410818 T^{2} + \)\(40\!\cdots\!01\)\( T^{4} \)
$19$ \( ( 1 + 949462 T + 6131066257801 T^{2} )^{2} \)
$23$ \( 1 - 75790028393378 T^{2} + \)\(17\!\cdots\!01\)\( T^{4} \)
$29$ \( 1 - 831288000078482 T^{2} + \)\(17\!\cdots\!01\)\( T^{4} \)
$31$ \( ( 1 + 29793118 T + 819628286980801 T^{2} )^{2} \)
$37$ \( ( 1 + 60811846 T + 4808584372417849 T^{2} )^{2} \)
$41$ \( 1 + 6157996032931678 T^{2} + \)\(18\!\cdots\!01\)\( T^{4} \)
$43$ \( ( 1 - 107419706 T + 21611482313284249 T^{2} )^{2} \)
$47$ \( 1 - 33376598707262018 T^{2} + \)\(27\!\cdots\!01\)\( T^{4} \)
$53$ \( 1 - 312876100791567218 T^{2} + \)\(30\!\cdots\!01\)\( T^{4} \)
$59$ \( 1 - 600827685707033522 T^{2} + \)\(26\!\cdots\!01\)\( T^{4} \)
$61$ \( ( 1 - 1030793642 T + 713342911662882601 T^{2} )^{2} \)
$67$ \( ( 1 - 1876742474 T + 1822837804551761449 T^{2} )^{2} \)
$71$ \( 1 + 690030731290713118 T^{2} + \)\(10\!\cdots\!01\)\( T^{4} \)
$73$ \( ( 1 + 2846528494 T + 4297625829703557649 T^{2} )^{2} \)
$79$ \( ( 1 - 1488647618 T + 9468276082626847201 T^{2} )^{2} \)
$83$ \( 1 - 29429698146400299218 T^{2} + \)\(24\!\cdots\!01\)\( T^{4} \)
$89$ \( 1 - 26116812713945754722 T^{2} + \)\(97\!\cdots\!01\)\( T^{4} \)
$97$ \( ( 1 + 1592948926 T + 73742412689492826049 T^{2} )^{2} \)
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