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Properties

Label 6.11.b
Level $6$
Weight $11$
Character orbit 6.b
Rep. character $\chi_{6}(5,\cdot)$
Character field $\Q$
Dimension $4$
Newform subspaces $1$
Sturm bound $11$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 6 = 2 \cdot 3 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 6.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(11\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(6, [\chi])\).

Total New Old
Modular forms 12 4 8
Cusp forms 8 4 4
Eisenstein series 4 0 4

Trace form

\( 4 q + 84 q^{3} - 2048 q^{4} + 5376 q^{6} - 45112 q^{7} + 159012 q^{9} + O(q^{10}) \) \( 4 q + 84 q^{3} - 2048 q^{4} + 5376 q^{6} - 45112 q^{7} + 159012 q^{9} - 53760 q^{10} - 43008 q^{12} + 275240 q^{13} - 1180800 q^{15} + 1048576 q^{16} - 2907648 q^{18} - 1568728 q^{19} + 9628008 q^{21} + 7730688 q^{22} - 2752512 q^{24} - 33732380 q^{25} + 34619508 q^{27} + 23097344 q^{28} - 85731840 q^{30} - 21785848 q^{31} + 25974144 q^{33} + 151087104 q^{34} - 81414144 q^{36} - 71014168 q^{37} + 217287240 q^{39} + 27525120 q^{40} - 145233408 q^{42} - 470688664 q^{43} + 312318720 q^{45} + 188814336 q^{46} + 22020096 q^{48} - 50058420 q^{49} - 708576768 q^{51} - 140922880 q^{52} + 481662720 q^{54} + 2701359360 q^{55} - 1058753208 q^{57} - 1564177920 q^{58} + 604569600 q^{60} - 1184038744 q^{61} - 905007096 q^{63} - 536870912 q^{64} + 3123445248 q^{66} - 297365848 q^{67} + 596268288 q^{69} - 3962250240 q^{70} + 1488715776 q^{72} + 6534269000 q^{73} - 5150031180 q^{75} + 803188736 q^{76} - 1322135040 q^{78} + 199282568 q^{79} + 1458964548 q^{81} + 8378668032 q^{82} - 4929540096 q^{84} - 12880512000 q^{85} + 210268800 q^{87} - 3958112256 q^{88} - 9243763200 q^{90} + 8317232080 q^{91} + 31744468392 q^{93} + 8505477120 q^{94} + 1409286144 q^{96} - 39176355064 q^{97} - 2626912512 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{11}^{\mathrm{new}}(6, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
6.11.b.a 6.b 3.b $4$ $3.812$ \(\Q(\sqrt{-2}, \sqrt{85})\) None \(0\) \(84\) \(0\) \(-45112\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(21-3\beta _{1}+\beta _{2})q^{3}-2^{9}q^{4}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(6, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(6, [\chi]) \cong \) \(S_{11}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 2}\)