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Properties

Label 11.11.d
Level $11$
Weight $11$
Character orbit 11.d
Rep. character $\chi_{11}(2,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $36$
Newform subspaces $1$
Sturm bound $11$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 11.d (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(11\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 44 44 0
Cusp forms 36 36 0
Eisenstein series 8 8 0

Trace form

\( 36 q - 5 q^{2} - 78 q^{3} + 2839 q^{4} + 566 q^{5} - 3525 q^{6} - 9740 q^{7} - 56325 q^{8} + 27883 q^{9} + O(q^{10}) \) \( 36 q - 5 q^{2} - 78 q^{3} + 2839 q^{4} + 566 q^{5} - 3525 q^{6} - 9740 q^{7} - 56325 q^{8} + 27883 q^{9} - 124277 q^{11} - 690462 q^{12} + 516610 q^{13} - 256990 q^{14} + 965070 q^{15} + 1558071 q^{16} - 1563930 q^{17} - 3716190 q^{18} + 6441265 q^{19} + 11846024 q^{20} - 38364515 q^{22} + 2991652 q^{23} - 6935455 q^{24} + 53140199 q^{25} + 53101970 q^{26} - 8464269 q^{27} - 158441860 q^{28} - 30773770 q^{29} + 164452420 q^{30} + 63499996 q^{31} - 337126483 q^{33} + 8404770 q^{34} + 93755030 q^{35} + 17054342 q^{36} - 20015352 q^{37} + 222215700 q^{38} + 13696700 q^{39} + 66388740 q^{40} + 168755230 q^{41} - 14778490 q^{42} + 1092554652 q^{44} - 1073801424 q^{45} - 843022850 q^{46} - 1466232 q^{47} - 1407287968 q^{48} - 247720591 q^{49} + 1888812255 q^{50} + 2730932925 q^{51} - 1016067090 q^{52} - 1574434638 q^{53} + 1667070934 q^{55} + 464386660 q^{56} - 1846600035 q^{57} - 5738108180 q^{58} - 3108186601 q^{59} + 1748753840 q^{60} + 4185015940 q^{61} + 8028589520 q^{62} + 5208740790 q^{63} - 568398521 q^{64} - 2767952130 q^{66} - 6673767122 q^{67} - 12578329400 q^{68} + 1374718982 q^{69} - 10858899380 q^{70} + 5532218182 q^{71} + 14192383525 q^{72} + 6815310530 q^{73} + 27099775830 q^{74} + 5359754505 q^{75} - 17322154610 q^{77} - 35448700760 q^{78} - 28511789960 q^{79} + 9512354316 q^{80} - 16645589156 q^{81} + 4251999505 q^{82} + 6078874665 q^{83} + 75048937530 q^{84} + 52883120010 q^{85} - 11116561805 q^{86} - 35103955205 q^{88} - 19181286322 q^{89} - 98405028320 q^{90} - 22561214930 q^{91} - 78730839752 q^{92} + 17679006934 q^{93} + 94886813720 q^{94} + 79444332050 q^{95} + 162737230420 q^{96} - 7866178077 q^{97} - 15303258335 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
11.11.d.a 11.d 11.d $36$ $6.989$ None \(-5\) \(-78\) \(566\) \(-9740\) $\mathrm{SU}(2)[C_{10}]$