Properties

Label 11.5.b
Level 11
Weight 5
Character orbit b
Rep. character \(\chi_{11}(10,\cdot)\)
Character field \(\Q\)
Dimension 3
Newform subspaces 2
Sturm bound 5
Trace bound 1

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Defining parameters

Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 11.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(5\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(11, [\chi])\).

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 0

Trace form

\( 3q + q^{3} - 12q^{4} + 13q^{5} - 176q^{9} + O(q^{10}) \) \( 3q + q^{3} - 12q^{4} + 13q^{5} - 176q^{9} + 143q^{11} + 196q^{12} + 600q^{14} - 529q^{15} - 312q^{16} - 1652q^{20} + 1320q^{22} + 721q^{23} + 2448q^{25} - 2040q^{26} + 127q^{27} - 3279q^{31} + 781q^{33} + 2520q^{34} + 1504q^{36} - 1779q^{37} - 1080q^{38} - 1800q^{42} + 1628q^{44} - 2896q^{45} + 1486q^{47} + 3496q^{48} + 1203q^{49} + 8326q^{53} - 5247q^{55} + 1200q^{56} - 13920q^{58} - 239q^{59} - 2884q^{60} + 10128q^{64} - 3960q^{66} - 13359q^{67} - 493q^{69} + 18600q^{70} + 14401q^{71} + 10416q^{75} - 13200q^{77} + 6120q^{78} - 30152q^{80} + 5965q^{81} - 11640q^{82} + 13200q^{86} + 2640q^{88} - 15779q^{89} + 20400q^{91} - 5084q^{92} + 4307q^{93} - 1299q^{97} - 5456q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(11, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
11.5.b.a \(1\) \(1.137\) \(\Q\) \(\Q(\sqrt{-11}) \) \(0\) \(7\) \(-49\) \(0\) \(q+7q^{3}+2^{4}q^{4}-7^{2}q^{5}-2^{5}q^{9}+11^{2}q^{11}+\cdots\)
11.5.b.b \(2\) \(1.137\) \(\Q(\sqrt{-30}) \) None \(0\) \(-6\) \(62\) \(0\) \(q+\beta q^{2}-3q^{3}-14q^{4}+31q^{5}-3\beta q^{6}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( ( 1 - 4 T )( 1 + 4 T ) \))(\( 1 - 2 T^{2} + 256 T^{4} \))
$3$ (\( 1 - 7 T + 81 T^{2} \))(\( ( 1 + 3 T + 81 T^{2} )^{2} \))
$5$ (\( 1 + 49 T + 625 T^{2} \))(\( ( 1 - 31 T + 625 T^{2} )^{2} \))
$7$ (\( ( 1 - 49 T )( 1 + 49 T ) \))(\( 1 - 1802 T^{2} + 5764801 T^{4} \))
$11$ (\( 1 - 121 T \))(\( 1 - 22 T + 14641 T^{2} \))
$13$ (\( ( 1 - 169 T )( 1 + 169 T ) \))(\( 1 - 22442 T^{2} + 815730721 T^{4} \))
$17$ (\( ( 1 - 289 T )( 1 + 289 T ) \))(\( 1 - 114122 T^{2} + 6975757441 T^{4} \))
$19$ (\( ( 1 - 361 T )( 1 + 361 T ) \))(\( 1 - 250922 T^{2} + 16983563041 T^{4} \))
$23$ (\( 1 - 167 T + 279841 T^{2} \))(\( ( 1 - 277 T + 279841 T^{2} )^{2} \))
$29$ (\( ( 1 - 841 T )( 1 + 841 T ) \))(\( ( 1 - 1102 T + 707281 T^{2} )( 1 + 1102 T + 707281 T^{2} ) \))
$31$ (\( 1 + 553 T + 923521 T^{2} \))(\( ( 1 + 1363 T + 923521 T^{2} )^{2} \))
$37$ (\( 1 + 2113 T + 1874161 T^{2} \))(\( ( 1 - 167 T + 1874161 T^{2} )^{2} \))
$41$ (\( ( 1 - 1681 T )( 1 + 1681 T ) \))(\( 1 - 4522442 T^{2} + 7984925229121 T^{4} \))
$43$ (\( ( 1 - 1849 T )( 1 + 1849 T ) \))(\( 1 - 5385602 T^{2} + 11688200277601 T^{4} \))
$47$ (\( 1 + 1918 T + 4879681 T^{2} \))(\( ( 1 - 1702 T + 4879681 T^{2} )^{2} \))
$53$ (\( 1 + 718 T + 7890481 T^{2} \))(\( ( 1 - 4522 T + 7890481 T^{2} )^{2} \))
$59$ (\( 1 - 4487 T + 12117361 T^{2} \))(\( ( 1 + 2363 T + 12117361 T^{2} )^{2} \))
$61$ (\( ( 1 - 3721 T )( 1 + 3721 T ) \))(\( 1 - 11966402 T^{2} + 191707312997281 T^{4} \))
$67$ (\( 1 + 7753 T + 20151121 T^{2} \))(\( ( 1 + 2803 T + 20151121 T^{2} )^{2} \))
$71$ (\( 1 - 7607 T + 25411681 T^{2} \))(\( ( 1 - 3397 T + 25411681 T^{2} )^{2} \))
$73$ (\( ( 1 - 5329 T )( 1 + 5329 T ) \))(\( 1 - 45779402 T^{2} + 806460091894081 T^{4} \))
$79$ (\( ( 1 - 6241 T )( 1 + 6241 T ) \))(\( 1 - 40803842 T^{2} + 1517108809906561 T^{4} \))
$83$ (\( ( 1 - 6889 T )( 1 + 6889 T ) \))(\( 1 - 94223522 T^{2} + 2252292232139041 T^{4} \))
$89$ (\( 1 + 6433 T + 62742241 T^{2} \))(\( ( 1 + 4673 T + 62742241 T^{2} )^{2} \))
$97$ (\( 1 + 9793 T + 88529281 T^{2} \))(\( ( 1 - 4247 T + 88529281 T^{2} )^{2} \))
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