# Properties

 Label 26.6.e Level $26$ Weight $6$ Character orbit 26.e Rep. character $\chi_{26}(17,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $12$ Newform subspaces $1$ Sturm bound $21$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$26 = 2 \cdot 13$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 26.e (of order $$6$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{6})$$ Newform subspaces: $$1$$ Sturm bound: $$21$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 40 12 28
Cusp forms 32 12 20
Eisenstein series 8 0 8

## Trace form

 $$12 q + 96 q^{4} + 360 q^{7} - 706 q^{9} + O(q^{10})$$ $$12 q + 96 q^{4} + 360 q^{7} - 706 q^{9} - 368 q^{10} + 504 q^{11} + 3202 q^{13} - 2272 q^{14} + 2112 q^{15} - 1536 q^{16} - 1910 q^{17} - 6888 q^{19} + 1440 q^{20} + 2160 q^{22} + 5920 q^{23} - 4672 q^{25} - 2320 q^{26} - 2736 q^{27} + 5760 q^{28} + 7922 q^{29} - 11696 q^{30} - 18780 q^{33} + 16864 q^{35} + 11296 q^{36} - 882 q^{37} + 26496 q^{38} + 48304 q^{39} - 11776 q^{40} + 44346 q^{41} + 23648 q^{42} - 41920 q^{43} - 158850 q^{45} - 33408 q^{46} + 4682 q^{49} + 11040 q^{50} + 133264 q^{51} + 43520 q^{52} - 187812 q^{53} + 1296 q^{54} + 17472 q^{55} - 18176 q^{56} - 73488 q^{58} + 74832 q^{59} + 27934 q^{61} - 4336 q^{62} + 156528 q^{63} - 49152 q^{64} + 69646 q^{65} + 6336 q^{66} + 85104 q^{67} + 30560 q^{68} - 77348 q^{69} - 106320 q^{71} - 78336 q^{72} + 96208 q^{74} + 192080 q^{75} - 110208 q^{76} - 151944 q^{77} + 9392 q^{78} + 30464 q^{79} + 23040 q^{80} - 72310 q^{81} - 87040 q^{82} + 53952 q^{84} - 148986 q^{85} - 121936 q^{87} - 34560 q^{88} + 93108 q^{89} + 282016 q^{90} - 56776 q^{91} + 189440 q^{92} + 107616 q^{93} + 158256 q^{94} + 232560 q^{95} + 147156 q^{97} + 46752 q^{98} + O(q^{100})$$

## 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.e.a $12$ $4.170$ $$\mathbb{Q}[x]/(x^{12} + \cdots)$$ None $$0$$ $$0$$ $$0$$ $$360$$ $$q-\beta _{4}q^{2}-\beta _{3}q^{3}+2^{4}\beta _{7}q^{4}+(5+\beta _{3}+\cdots)q^{5}+\cdots$$

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

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