# Properties

 Label 26.3.d Level 26 Weight 3 Character orbit d Rep. character $$\chi_{26}(5,\cdot)$$ Character field $$\Q(\zeta_{4})$$ Dimension 2 Newform subspaces 1 Sturm bound 10 Trace bound 0

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$26 = 2 \cdot 13$$ Weight: $$k$$ $$=$$ $$3$$ Character orbit: $$[\chi]$$ $$=$$ 26.d (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$13$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$10$$ Trace bound: $$0$$

## Dimensions

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

Total New Old
Modular forms 18 2 16
Cusp forms 10 2 8
Eisenstein series 8 0 8

## Trace form

 $$2q + 2q^{2} - 6q^{5} + 4q^{7} - 4q^{8} - 18q^{9} + O(q^{10})$$ $$2q + 2q^{2} - 6q^{5} + 4q^{7} - 4q^{8} - 18q^{9} + 12q^{11} + 8q^{14} - 8q^{16} - 18q^{18} + 52q^{19} + 12q^{20} + 24q^{22} - 26q^{26} + 8q^{28} - 96q^{29} - 28q^{31} - 8q^{32} - 12q^{34} - 24q^{35} + 74q^{37} + 24q^{40} - 18q^{41} + 24q^{44} + 54q^{45} + 48q^{46} + 84q^{47} + 14q^{50} - 52q^{52} + 60q^{53} - 72q^{55} - 96q^{58} - 108q^{59} - 36q^{61} - 36q^{63} + 78q^{65} - 44q^{67} - 24q^{68} - 24q^{70} + 12q^{71} + 36q^{72} + 34q^{73} + 148q^{74} - 104q^{76} - 216q^{79} + 24q^{80} + 162q^{81} + 156q^{83} + 36q^{85} - 72q^{86} - 18q^{89} + 52q^{91} + 96q^{92} + 168q^{94} - 94q^{97} - 82q^{98} - 108q^{99} + O(q^{100})$$

## 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.d.a $$2$$ $$0.708$$ $$\Q(\sqrt{-1})$$ None $$2$$ $$0$$ $$-6$$ $$4$$ $$q+(1+i)q^{2}+2iq^{4}+(-3-3i)q^{5}+\cdots$$

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

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

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 - 2 T + 2 T^{2}$$
$3$ $$( 1 + 9 T^{2} )^{2}$$
$5$ $$1 + 6 T + 18 T^{2} + 150 T^{3} + 625 T^{4}$$
$7$ $$1 - 4 T + 8 T^{2} - 196 T^{3} + 2401 T^{4}$$
$11$ $$1 - 12 T + 72 T^{2} - 1452 T^{3} + 14641 T^{4}$$
$13$ $$1 + 169 T^{2}$$
$17$ $$1 - 542 T^{2} + 83521 T^{4}$$
$19$ $$1 - 52 T + 1352 T^{2} - 18772 T^{3} + 130321 T^{4}$$
$23$ $$1 - 482 T^{2} + 279841 T^{4}$$
$29$ $$( 1 + 48 T + 841 T^{2} )^{2}$$
$31$ $$1 + 28 T + 392 T^{2} + 26908 T^{3} + 923521 T^{4}$$
$37$ $$( 1 - 37 T )^{2}( 1 + 1369 T^{2} )$$
$41$ $$1 + 18 T + 162 T^{2} + 30258 T^{3} + 2825761 T^{4}$$
$43$ $$1 - 2402 T^{2} + 3418801 T^{4}$$
$47$ $$1 - 84 T + 3528 T^{2} - 185556 T^{3} + 4879681 T^{4}$$
$53$ $$( 1 - 30 T + 2809 T^{2} )^{2}$$
$59$ $$1 + 108 T + 5832 T^{2} + 375948 T^{3} + 12117361 T^{4}$$
$61$ $$( 1 + 18 T + 3721 T^{2} )^{2}$$
$67$ $$1 + 44 T + 968 T^{2} + 197516 T^{3} + 20151121 T^{4}$$
$71$ $$1 - 12 T + 72 T^{2} - 60492 T^{3} + 25411681 T^{4}$$
$73$ $$1 - 34 T + 578 T^{2} - 181186 T^{3} + 28398241 T^{4}$$
$79$ $$( 1 + 108 T + 6241 T^{2} )^{2}$$
$83$ $$1 - 156 T + 12168 T^{2} - 1074684 T^{3} + 47458321 T^{4}$$
$89$ $$1 + 18 T + 162 T^{2} + 142578 T^{3} + 62742241 T^{4}$$
$97$ $$1 + 94 T + 4418 T^{2} + 884446 T^{3} + 88529281 T^{4}$$