# 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

# Related objects

## 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

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