# Properties

 Label 26.6.c Level $26$ Weight $6$ Character orbit 26.c Rep. character $\chi_{26}(3,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $14$ Newform subspaces $2$ Sturm bound $21$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$26 = 2 \cdot 13$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 26.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$2$$ Sturm bound: $$21$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{6}(26, [\chi])$$.

Total New Old
Modular forms 38 14 24
Cusp forms 30 14 16
Eisenstein series 8 0 8

## Trace form

 $$14 q + 4 q^{2} - 112 q^{4} - 22 q^{5} - 76 q^{7} - 128 q^{8} - 671 q^{9} + O(q^{10})$$ $$14 q + 4 q^{2} - 112 q^{4} - 22 q^{5} - 76 q^{7} - 128 q^{8} - 671 q^{9} - 52 q^{10} + 948 q^{11} + 293 q^{13} + 2624 q^{14} - 1984 q^{15} - 1792 q^{16} - 725 q^{17} - 1960 q^{18} + 2984 q^{19} + 176 q^{20} + 3176 q^{21} + 224 q^{22} - 4844 q^{23} + 22864 q^{25} + 708 q^{26} - 2736 q^{27} - 1216 q^{28} + 1639 q^{29} - 1616 q^{30} - 40184 q^{31} + 1024 q^{32} - 31900 q^{33} - 2200 q^{34} + 20516 q^{35} - 10736 q^{36} + 12395 q^{37} + 40896 q^{38} + 21168 q^{39} + 1664 q^{40} - 15497 q^{41} + 2848 q^{42} - 7768 q^{43} - 30336 q^{44} + 43303 q^{45} - 21744 q^{46} - 28368 q^{47} - 96075 q^{49} + 33424 q^{50} + 183728 q^{51} + 1376 q^{52} + 82570 q^{53} - 67248 q^{54} - 50092 q^{55} - 20992 q^{56} - 92536 q^{57} + 39468 q^{58} - 99036 q^{59} + 63488 q^{60} + 18215 q^{61} - 19776 q^{62} + 101484 q^{63} + 57344 q^{64} + 7011 q^{65} + 99520 q^{66} - 54644 q^{67} - 11600 q^{68} - 5748 q^{69} - 126688 q^{70} - 15272 q^{71} + 15680 q^{72} - 58862 q^{73} - 80484 q^{74} - 82880 q^{75} + 47744 q^{76} + 236424 q^{77} - 210000 q^{78} - 340616 q^{79} + 2816 q^{80} + 130513 q^{81} - 13540 q^{82} + 51360 q^{83} - 25408 q^{84} - 32119 q^{85} + 139232 q^{86} + 207120 q^{87} + 3584 q^{88} - 178754 q^{89} + 53000 q^{90} + 221120 q^{91} + 155008 q^{92} + 356856 q^{93} - 115504 q^{94} + 235024 q^{95} + 97142 q^{97} + 376452 q^{98} - 354584 q^{99} + O(q^{100})$$

## Decomposition of $$S_{6}^{\mathrm{new}}(26, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
26.6.c.a $6$ $4.170$ $$\mathbb{Q}[x]/(x^{6} + \cdots)$$ None $$-12$$ $$0$$ $$2$$ $$-202$$ $$q-4\beta _{1}q^{2}+\beta _{3}q^{3}+(-2^{4}+2^{4}\beta _{1}+\cdots)q^{4}+\cdots$$
26.6.c.b $8$ $4.170$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$16$$ $$0$$ $$-24$$ $$126$$ $$q+(4+4\beta _{2})q^{2}-\beta _{1}q^{3}+2^{4}\beta _{2}q^{4}+\cdots$$

## Decomposition of $$S_{6}^{\mathrm{old}}(26, [\chi])$$ into lower level spaces

$$S_{6}^{\mathrm{old}}(26, [\chi]) \simeq$$ $$S_{6}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 2}$$