Properties

Label 11.13.d
Level $11$
Weight $13$
Character orbit 11.d
Rep. character $\chi_{11}(2,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $44$
Newform subspaces $1$
Sturm bound $13$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 13 \)
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: \(13\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{13}(11, [\chi])\).

Total New Old
Modular forms 52 52 0
Cusp forms 44 44 0
Eisenstein series 8 8 0

Trace form

\( 44 q - 5 q^{2} - 1083 q^{3} + 16247 q^{4} - 723 q^{5} + 147195 q^{6} - 219605 q^{7} + 921595 q^{8} - 3695582 q^{9} + O(q^{10}) \) \( 44 q - 5 q^{2} - 1083 q^{3} + 16247 q^{4} - 723 q^{5} + 147195 q^{6} - 219605 q^{7} + 921595 q^{8} - 3695582 q^{9} + 2565608 q^{11} + 7500402 q^{12} - 6670805 q^{13} - 249422 q^{14} + 31344279 q^{15} - 182249929 q^{16} - 7887605 q^{17} + 296147970 q^{18} - 59195705 q^{19} - 119854528 q^{20} + 615523885 q^{22} - 407959208 q^{23} + 217767665 q^{24} - 1102003838 q^{25} - 1289107598 q^{26} + 945406779 q^{27} + 5018997220 q^{28} - 541321205 q^{29} - 7192403540 q^{30} + 1789230381 q^{31} + 8868147617 q^{33} + 4668584258 q^{34} - 3628416965 q^{35} - 18485968210 q^{36} - 7637278083 q^{37} - 1555712420 q^{38} + 24275524235 q^{39} + 17352998460 q^{40} - 20307362045 q^{41} - 51939651970 q^{42} + 73504485716 q^{44} + 33796434396 q^{45} - 10698599530 q^{46} - 13177100523 q^{47} - 48055484488 q^{48} - 11538977128 q^{49} + 8631835695 q^{50} + 103295029335 q^{51} - 124762325930 q^{52} + 80932774677 q^{53} - 87742505883 q^{55} - 162644024476 q^{56} + 156654446895 q^{57} + 68439789940 q^{58} + 153452464089 q^{59} + 211654410344 q^{60} - 130004870645 q^{61} - 478111392680 q^{62} + 56162082000 q^{63} + 88053755815 q^{64} - 547107987930 q^{66} + 172356405472 q^{67} + 550428178040 q^{68} + 147718471202 q^{69} + 656066411580 q^{70} - 276485879307 q^{71} - 1923582671435 q^{72} + 401204208595 q^{73} + 668106311350 q^{74} + 545281450749 q^{75} - 431450680685 q^{77} + 349062971320 q^{78} + 454959862075 q^{79} + 732789378812 q^{80} + 681177766216 q^{81} + 455720922385 q^{82} - 1768304661305 q^{83} - 2152859747190 q^{84} - 2586009108005 q^{85} - 686286163053 q^{86} + 2647326267355 q^{88} + 587790027856 q^{89} + 6704158241200 q^{90} - 245650237373 q^{91} + 3006033812992 q^{92} + 794315205079 q^{93} - 1053727188680 q^{94} - 7101305012165 q^{95} - 13699998107060 q^{96} + 647608267617 q^{97} + 6944343091354 q^{99} + O(q^{100}) \)

Decomposition of \(S_{13}^{\mathrm{new}}(11, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
11.13.d.a 11.d 11.d $44$ $10.054$ None \(-5\) \(-1083\) \(-723\) \(-219605\) $\mathrm{SU}(2)[C_{10}]$