# Properties

 Label 26.4.e Level $26$ Weight $4$ Character orbit 26.e Rep. character $\chi_{26}(17,\cdot)$ Character field $\Q(\zeta_{6})$ Dimension $8$ Newform subspaces $1$ Sturm bound $14$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$26 = 2 \cdot 13$$ Weight: $$k$$ $$=$$ $$4$$ 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: $$14$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(26, [\chi])$$.

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

## Trace form

 $$8 q - 6 q^{3} + 16 q^{4} + 18 q^{7} - 22 q^{9} + O(q^{10})$$ $$8 q - 6 q^{3} + 16 q^{4} + 18 q^{7} - 22 q^{9} - 8 q^{10} - 18 q^{11} - 48 q^{12} - 130 q^{13} + 80 q^{14} - 192 q^{15} - 64 q^{16} + 112 q^{17} + 594 q^{19} + 72 q^{20} - 72 q^{22} - 230 q^{23} - 180 q^{25} - 184 q^{26} + 468 q^{27} + 72 q^{28} + 32 q^{29} + 328 q^{30} - 42 q^{33} - 128 q^{35} + 88 q^{36} - 768 q^{37} - 576 q^{38} - 230 q^{39} - 64 q^{40} - 564 q^{41} - 688 q^{42} - 114 q^{43} + 630 q^{45} + 576 q^{46} - 96 q^{48} - 110 q^{49} + 1968 q^{50} + 1300 q^{51} - 104 q^{52} + 36 q^{53} + 648 q^{54} + 1248 q^{55} + 160 q^{56} - 1848 q^{58} - 1110 q^{59} + 900 q^{61} + 1064 q^{62} - 1980 q^{63} - 512 q^{64} + 1870 q^{65} - 2400 q^{66} + 510 q^{67} - 448 q^{68} - 2402 q^{69} - 1470 q^{71} + 576 q^{72} - 680 q^{74} - 862 q^{75} + 2376 q^{76} + 2340 q^{77} + 1016 q^{78} + 784 q^{79} + 288 q^{80} + 1868 q^{81} + 704 q^{82} - 2136 q^{84} - 2898 q^{85} + 1598 q^{87} + 288 q^{88} - 4434 q^{89} - 2384 q^{90} - 886 q^{91} - 1840 q^{92} + 3108 q^{93} - 2568 q^{94} - 816 q^{95} + 1854 q^{97} + 4272 q^{98} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(26, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
26.4.e.a $8$ $1.534$ $$\mathbb{Q}[x]/(x^{8} + \cdots)$$ None $$0$$ $$-6$$ $$0$$ $$18$$ $$q-\beta _{3}q^{2}+(-2+2\beta _{1}+\beta _{4}-\beta _{7})q^{3}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(26, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(26, [\chi]) \simeq$$ $$S_{4}^{\mathrm{new}}(13, [\chi])$$$$^{\oplus 2}$$