# Properties

 Label 26.6.b Level $26$ Weight $6$ Character orbit 26.b Rep. character $\chi_{26}(25,\cdot)$ Character field $\Q$ Dimension $4$ Newform subspaces $2$ Sturm bound $21$ Trace bound $3$

# Related objects

## Defining parameters

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

## Dimensions

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

Total New Old
Modular forms 20 4 16
Cusp forms 16 4 12
Eisenstein series 4 0 4

## Trace form

 $$4 q - 18 q^{3} - 64 q^{4} - 602 q^{9} + O(q^{10})$$ $$4 q - 18 q^{3} - 64 q^{4} - 602 q^{9} - 136 q^{10} + 288 q^{12} - 182 q^{13} + 184 q^{14} + 1024 q^{16} + 1274 q^{17} - 2160 q^{22} + 6308 q^{23} - 1950 q^{25} + 3640 q^{26} + 4482 q^{27} - 11588 q^{29} - 7480 q^{30} - 21862 q^{35} + 9632 q^{36} - 768 q^{38} + 19604 q^{39} + 2176 q^{40} - 13544 q^{42} - 13842 q^{43} - 4608 q^{48} + 31730 q^{49} + 42530 q^{51} + 2912 q^{52} + 74928 q^{53} - 65280 q^{55} - 2944 q^{56} - 126756 q^{61} + 88432 q^{62} - 16384 q^{64} + 34034 q^{65} - 24960 q^{66} - 20384 q^{68} - 10468 q^{69} - 1144 q^{74} - 25616 q^{75} - 89160 q^{77} - 1352 q^{78} + 35684 q^{79} + 24100 q^{81} - 129920 q^{82} + 93184 q^{87} + 34560 q^{88} + 93296 q^{90} + 30862 q^{91} - 100928 q^{92} + 177720 q^{94} + 265404 q^{95} + O(q^{100})$$

## 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.b.a $2$ $4.170$ $$\Q(\sqrt{-1})$$ None $$0$$ $$-26$$ $$0$$ $$0$$ $$q+4iq^{2}-13q^{3}-2^{4}q^{4}-51iq^{5}+\cdots$$
26.6.b.b $2$ $4.170$ $$\Q(\sqrt{-1})$$ None $$0$$ $$8$$ $$0$$ $$0$$ $$q+2iq^{2}+4q^{3}-2^{4}q^{4}+34iq^{5}+\cdots$$

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

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