# Properties

 Label 26.3.f Level $26$ Weight $3$ Character orbit 26.f Rep. character $\chi_{26}(7,\cdot)$ Character field $\Q(\zeta_{12})$ Dimension $12$ Newform subspaces $2$ Sturm bound $10$ Trace bound $1$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$26 = 2 \cdot 13$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 26.f (of order $$12$$ and degree $$4$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(\zeta_{12})$$ Newform subspaces: $$2$$ Sturm bound: $$10$$ Trace bound: $$1$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{3}(26, [\chi])$$.

Total New Old
Modular forms 36 12 24
Cusp forms 20 12 8
Eisenstein series 16 0 16

## Trace form

 $$12 q - 2 q^{2} + 6 q^{5} - 24 q^{7} - 8 q^{8} - 30 q^{9} + O(q^{10})$$ $$12 q - 2 q^{2} + 6 q^{5} - 24 q^{7} - 8 q^{8} - 30 q^{9} - 30 q^{10} - 24 q^{11} + 24 q^{13} + 16 q^{14} + 72 q^{15} + 24 q^{16} + 36 q^{17} + 108 q^{18} - 12 q^{19} + 12 q^{20} - 60 q^{21} - 24 q^{22} - 24 q^{23} + 26 q^{26} + 72 q^{27} - 48 q^{28} - 60 q^{29} - 192 q^{30} - 96 q^{31} + 8 q^{32} + 12 q^{33} - 84 q^{34} - 36 q^{35} - 48 q^{36} - 66 q^{37} - 24 q^{40} + 132 q^{41} + 144 q^{42} + 12 q^{43} + 120 q^{44} + 276 q^{45} + 144 q^{46} + 192 q^{47} + 300 q^{49} + 232 q^{50} + 72 q^{52} - 300 q^{53} - 360 q^{54} - 156 q^{55} - 96 q^{56} - 396 q^{57} - 66 q^{58} + 24 q^{59} - 96 q^{60} + 114 q^{61} - 72 q^{62} - 192 q^{63} - 420 q^{65} + 96 q^{66} + 12 q^{67} + 36 q^{68} + 132 q^{69} + 240 q^{70} - 132 q^{71} + 156 q^{72} + 30 q^{73} - 70 q^{74} + 120 q^{75} + 24 q^{76} + 216 q^{78} + 96 q^{79} + 24 q^{80} - 30 q^{81} - 330 q^{82} - 48 q^{83} - 168 q^{84} - 66 q^{85} - 24 q^{86} + 264 q^{87} + 234 q^{89} + 336 q^{91} - 48 q^{92} + 492 q^{93} + 72 q^{94} + 672 q^{95} + 222 q^{97} - 158 q^{98} + 144 q^{99} + O(q^{100})$$

## Decomposition of $$S_{3}^{\mathrm{new}}(26, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
26.3.f.a $4$ $0.708$ $$\Q(\zeta_{12})$$ None $$2$$ $$0$$ $$0$$ $$-22$$ $$q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots$$
26.3.f.b $8$ $0.708$ 8.0.$$\cdots$$.1 None $$-4$$ $$0$$ $$6$$ $$-2$$ $$q+(-\beta _{3}-\beta _{4})q^{2}+(-\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots$$

## Decomposition of $$S_{3}^{\mathrm{old}}(26, [\chi])$$ into lower level spaces

$$S_{3}^{\mathrm{old}}(26, [\chi]) \cong$$ $$S_{3}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 2}$$