# Properties

 Label 11.6.c Level $11$ Weight $6$ Character orbit 11.c Rep. character $\chi_{11}(3,\cdot)$ Character field $\Q(\zeta_{5})$ Dimension $16$ Newform subspaces $1$ Sturm bound $6$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$11$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 11.c (of order $$5$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$11$$ Character field: $$\Q(\zeta_{5})$$ Newform subspaces: $$1$$ Sturm bound: $$6$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 24 24 0
Cusp forms 16 16 0
Eisenstein series 8 8 0

## Trace form

 $$16 q - q^{2} - 24 q^{3} - 73 q^{4} - 10 q^{5} + 121 q^{6} + 196 q^{7} + 527 q^{8} - 530 q^{9} + O(q^{10})$$ $$16 q - q^{2} - 24 q^{3} - 73 q^{4} - 10 q^{5} + 121 q^{6} + 196 q^{7} + 527 q^{8} - 530 q^{9} - 672 q^{10} - 692 q^{11} - 1562 q^{12} + 1162 q^{13} + 560 q^{14} + 1796 q^{15} + 6399 q^{16} - 22 q^{17} + 834 q^{18} - 3236 q^{19} - 5514 q^{20} - 7772 q^{21} - 13059 q^{22} - 10848 q^{23} + 13233 q^{24} + 15686 q^{25} + 16216 q^{26} + 22500 q^{27} + 8838 q^{28} + 13070 q^{29} - 22830 q^{30} - 14764 q^{31} - 58812 q^{32} - 48544 q^{33} - 26966 q^{34} + 43368 q^{35} + 63696 q^{36} + 4638 q^{37} + 68144 q^{38} + 20300 q^{39} + 52284 q^{40} - 14806 q^{41} - 69922 q^{42} - 24376 q^{43} - 104960 q^{44} - 97480 q^{45} + 50452 q^{46} + 40364 q^{47} + 30236 q^{48} + 32246 q^{49} + 10839 q^{50} + 75564 q^{51} - 80654 q^{52} - 11654 q^{53} + 43796 q^{54} + 7052 q^{55} + 70632 q^{56} - 40020 q^{57} + 10276 q^{58} + 70804 q^{59} + 46116 q^{60} - 31446 q^{61} - 153388 q^{62} - 7064 q^{63} + 17695 q^{64} - 41284 q^{65} + 48006 q^{66} - 64200 q^{67} - 94114 q^{68} - 62412 q^{69} - 103768 q^{70} - 184380 q^{71} - 14729 q^{72} - 1750 q^{73} + 306048 q^{74} + 246596 q^{75} + 174806 q^{76} + 384646 q^{77} + 360916 q^{78} + 24324 q^{79} - 386444 q^{80} - 259412 q^{81} - 316255 q^{82} - 46028 q^{83} - 271956 q^{84} + 63914 q^{85} + 22931 q^{86} - 47592 q^{87} + 211871 q^{88} + 148364 q^{89} - 347186 q^{90} - 258448 q^{91} - 58658 q^{92} - 387478 q^{93} - 55370 q^{94} - 4716 q^{95} + 328396 q^{96} + 484296 q^{97} + 743692 q^{98} + 724964 q^{99} + O(q^{100})$$

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

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
11.6.c.a $16$ $1.764$ $$\mathbb{Q}[x]/(x^{16} - \cdots)$$ None $$-1$$ $$-24$$ $$-10$$ $$196$$ $$q+(1-\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{7})q^{2}+\cdots$$