# Properties

 Label 5.13.c Level $5$ Weight $13$ Character orbit 5.c Rep. character $\chi_{5}(2,\cdot)$ Character field $\Q(\zeta_{4})$ Dimension $10$ Newform subspaces $1$ Sturm bound $6$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$5$$ Weight: $$k$$ $$=$$ $$13$$ Character orbit: $$[\chi]$$ $$=$$ 5.c (of order $$4$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$5$$ Character field: $$\Q(i)$$ Newform subspaces: $$1$$ Sturm bound: $$6$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{13}(5, [\chi])$$.

Total New Old
Modular forms 14 14 0
Cusp forms 10 10 0
Eisenstein series 4 4 0

## Trace form

 $$10 q - 2 q^{2} + 318 q^{3} - 4250 q^{5} - 175080 q^{6} + 279598 q^{7} - 469980 q^{8} + O(q^{10})$$ $$10 q - 2 q^{2} + 318 q^{3} - 4250 q^{5} - 175080 q^{6} + 279598 q^{7} - 469980 q^{8} + 1552150 q^{10} + 312620 q^{11} - 2359992 q^{12} + 5290738 q^{13} - 5821650 q^{15} + 30547960 q^{16} - 41269502 q^{17} - 140573742 q^{18} + 334988100 q^{20} + 107493420 q^{21} - 155490544 q^{22} - 510099842 q^{23} + 942201250 q^{25} + 1475846420 q^{26} - 1993958640 q^{27} - 3562106488 q^{28} + 5922516000 q^{30} + 3077089820 q^{31} - 4623883832 q^{32} - 7503698004 q^{33} + 9330787150 q^{35} + 7760793660 q^{36} - 2599618502 q^{37} - 15310240920 q^{38} + 15901243500 q^{40} + 7412079020 q^{41} - 18593270064 q^{42} - 5784410402 q^{43} - 10510145100 q^{45} - 7382547880 q^{46} + 16053249598 q^{47} + 42572492208 q^{48} - 68314688750 q^{50} - 33139878180 q^{51} + 96763417228 q^{52} + 101763514618 q^{53} - 84180068500 q^{55} - 172002747600 q^{56} + 27733489920 q^{57} + 135238672320 q^{58} - 220124568600 q^{60} + 7731718220 q^{61} + 193287375176 q^{62} + 207465112158 q^{63} - 338075024150 q^{65} - 60815472960 q^{66} - 80010636002 q^{67} + 204699541412 q^{68} + 376969924200 q^{70} - 46557252580 q^{71} - 13986370620 q^{72} - 448527032342 q^{73} + 719724648750 q^{75} + 305095930800 q^{76} - 425580405844 q^{77} - 1690993241784 q^{78} + 873032236000 q^{80} + 1107831051810 q^{81} - 671946416464 q^{82} - 91118376722 q^{83} + 543768569650 q^{85} + 414117747320 q^{86} - 2078422804320 q^{87} - 1842434230560 q^{88} + 3098742811350 q^{90} + 2737742572220 q^{91} + 906853941448 q^{92} - 91295366484 q^{93} - 1044695070000 q^{95} - 3473259523680 q^{96} - 1409507601302 q^{97} - 1481746533298 q^{98} + O(q^{100})$$

## Decomposition of $$S_{13}^{\mathrm{new}}(5, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
5.13.c.a $10$ $4.570$ $$\mathbb{Q}[x]/(x^{10} + \cdots)$$ None $$-2$$ $$318$$ $$-4250$$ $$279598$$ $$q+\beta _{5}q^{2}+(31-31\beta _{1}-\beta _{3}+3\beta _{6}+\cdots)q^{3}+\cdots$$