# 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 $0$

# Related objects

## 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

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

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

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
6.11.b.a $$4$$ $$3.812$$ $$\Q(\sqrt{-2}, \sqrt{85})$$ None $$0$$ $$84$$ $$0$$ $$-45112$$ $$q+\beta _{1}q^{2}+(21-3\beta _{1}+\beta _{2})q^{3}-2^{9}q^{4}+\cdots$$

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

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