# Properties

 Label 7.6.c Level $7$ Weight $6$ Character orbit 7.c Rep. character $\chi_{7}(2,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $4$ Newform subspaces $1$ Sturm bound $4$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$7$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 7.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$1$$ Sturm bound: $$4$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(7, [\chi])$$.

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

## Trace form

 $$4 q - 2 q^{2} + 8 q^{3} - 12 q^{4} + 38 q^{5} - 164 q^{6} - 168 q^{7} + 192 q^{8} + 380 q^{9} + O(q^{10})$$ $$4 q - 2 q^{2} + 8 q^{3} - 12 q^{4} + 38 q^{5} - 164 q^{6} - 168 q^{7} + 192 q^{8} + 380 q^{9} + 778 q^{10} - 424 q^{11} + 196 q^{12} - 1848 q^{13} - 2674 q^{14} + 1784 q^{15} + 2064 q^{16} + 2346 q^{17} - 212 q^{18} + 360 q^{19} - 3416 q^{20} - 1526 q^{21} + 4252 q^{22} + 12 q^{23} - 1392 q^{24} - 1872 q^{25} - 1148 q^{26} + 5744 q^{27} + 2548 q^{28} - 14104 q^{29} - 5258 q^{30} - 3548 q^{31} + 8096 q^{32} + 3398 q^{33} + 14844 q^{34} + 27496 q^{35} - 2192 q^{36} - 11090 q^{37} - 20138 q^{38} - 1624 q^{39} - 15936 q^{40} + 7000 q^{41} - 3472 q^{42} - 25360 q^{43} - 5948 q^{44} - 1300 q^{45} + 5118 q^{46} + 22956 q^{47} + 22432 q^{48} + 4900 q^{49} + 59984 q^{50} + 384 q^{51} + 1400 q^{52} - 3042 q^{53} - 32546 q^{54} - 50152 q^{55} - 57792 q^{56} - 38116 q^{57} + 58852 q^{58} + 65808 q^{59} - 14084 q^{60} + 42486 q^{61} - 98724 q^{62} - 4760 q^{63} + 70912 q^{64} + 3164 q^{65} + 25894 q^{66} - 42312 q^{67} - 5460 q^{68} + 10308 q^{69} - 113050 q^{70} - 4416 q^{71} + 32448 q^{72} + 50506 q^{73} + 47370 q^{74} + 35608 q^{75} + 77672 q^{76} + 65338 q^{77} + 55048 q^{78} - 9004 q^{79} - 68816 q^{80} - 51178 q^{81} - 67732 q^{82} - 208656 q^{83} + 44492 q^{84} - 106212 q^{85} - 86776 q^{86} - 80008 q^{87} + 20496 q^{88} + 26666 q^{89} + 261304 q^{90} + 135632 q^{91} - 20568 q^{92} - 38718 q^{93} - 98034 q^{94} + 198140 q^{95} - 54880 q^{96} + 418264 q^{97} + 98686 q^{98} - 133888 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(7, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
7.6.c.a $4$ $1.123$ $$\Q(\sqrt{-3}, \sqrt{37})$$ None $$-2$$ $$8$$ $$38$$ $$-168$$ $$q+(-\beta _{1}-\beta _{2})q^{2}+(4-4\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots$$