# Properties

 Label 7.10.c Level $7$ Weight $10$ Character orbit 7.c Rep. character $\chi_{7}(2,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $10$ Newform subspaces $1$ Sturm bound $6$ Trace bound $0$

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## Defining parameters

 Level: $$N$$ $$=$$ $$7$$ Weight: $$k$$ $$=$$ $$10$$ Character orbit: $$[\chi]$$ $$=$$ 7.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$1$$ Sturm bound: $$6$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{10}(7, [\chi])$$.

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

## Trace form

 $$10 q - 18 q^{2} + 161 q^{3} - 940 q^{4} + 1533 q^{5} - 8708 q^{6} - 1036 q^{7} + 34272 q^{8} - 35734 q^{9} + O(q^{10})$$ $$10 q - 18 q^{2} + 161 q^{3} - 940 q^{4} + 1533 q^{5} - 8708 q^{6} - 1036 q^{7} + 34272 q^{8} - 35734 q^{9} + 4298 q^{10} + 42213 q^{11} + 135604 q^{12} - 319676 q^{13} - 39522 q^{14} + 151394 q^{15} + 322064 q^{16} + 324681 q^{17} - 1012868 q^{18} - 16121 q^{19} - 350616 q^{20} - 1557857 q^{21} - 62692 q^{22} + 2638863 q^{23} + 8449728 q^{24} - 1304092 q^{25} + 4179252 q^{26} - 18331558 q^{27} - 22156316 q^{28} + 15292500 q^{29} + 20557942 q^{30} + 19179237 q^{31} - 6263520 q^{32} + 1689359 q^{33} - 62909700 q^{34} - 43746759 q^{35} + 71476528 q^{36} + 39566985 q^{37} + 67365270 q^{38} - 44299486 q^{39} + 5721744 q^{40} - 53436852 q^{41} - 183129856 q^{42} + 101835992 q^{43} + 99704916 q^{44} + 85098230 q^{45} - 14489202 q^{46} + 32509659 q^{47} - 185141600 q^{48} - 49024598 q^{49} + 3328464 q^{50} + 44168403 q^{51} + 103893272 q^{52} - 25714707 q^{53} + 51200926 q^{54} - 144695222 q^{55} + 115352832 q^{56} - 121710346 q^{57} - 46645516 q^{58} + 46776513 q^{59} + 132391756 q^{60} - 113075039 q^{61} + 467465628 q^{62} + 318071530 q^{63} - 192008960 q^{64} - 338113566 q^{65} - 836682602 q^{66} - 126707879 q^{67} + 32262636 q^{68} + 1323616182 q^{69} + 697712470 q^{70} - 1188736032 q^{71} - 950557728 q^{72} - 859257651 q^{73} + 591757530 q^{74} - 169061732 q^{75} + 1101475592 q^{76} + 1911891891 q^{77} + 519432424 q^{78} - 527065417 q^{79} - 1257352656 q^{80} + 551662715 q^{81} - 1341703076 q^{82} - 144863208 q^{83} + 486452204 q^{84} - 1197360222 q^{85} - 678648216 q^{86} - 340781350 q^{87} + 903700608 q^{88} + 1661554797 q^{89} + 1967758744 q^{90} + 726641384 q^{91} - 1301840952 q^{92} - 423057489 q^{93} - 272580882 q^{94} - 1197123495 q^{95} - 1441922272 q^{96} + 869770188 q^{97} - 2404833858 q^{98} - 1900777180 q^{99} + O(q^{100})$$

## Decomposition of $$S_{10}^{\mathrm{new}}(7, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
7.10.c.a $10$ $3.605$ $$\mathbb{Q}[x]/(x^{10} - \cdots)$$ None $$-18$$ $$161$$ $$1533$$ $$-1036$$ $$q+(-\beta _{1}+\beta _{2}-4\beta _{3})q^{2}+(33-\beta _{1}+\cdots)q^{3}+\cdots$$