# Properties

 Label 14.10.c Level $14$ Weight $10$ Character orbit 14.c Rep. character $\chi_{14}(9,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $12$ Newform subspaces $2$ Sturm bound $20$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$14 = 2 \cdot 7$$ Weight: $$k$$ $$=$$ $$10$$ Character orbit: $$[\chi]$$ $$=$$ 14.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$7$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$2$$ Sturm bound: $$20$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{10}(14, [\chi])$$.

Total New Old
Modular forms 40 12 28
Cusp forms 32 12 20
Eisenstein series 8 0 8

## Trace form

 $$12 q - 162 q^{3} - 1536 q^{4} - 1818 q^{5} + 9728 q^{6} - 1784 q^{7} - 24164 q^{9} + O(q^{10})$$ $$12 q - 162 q^{3} - 1536 q^{4} - 1818 q^{5} + 9728 q^{6} - 1784 q^{7} - 24164 q^{9} + 5632 q^{10} + 9894 q^{11} - 41472 q^{12} + 233176 q^{13} - 99072 q^{14} + 32092 q^{15} - 393216 q^{16} - 285906 q^{17} - 95232 q^{18} + 842658 q^{19} + 930816 q^{20} + 365650 q^{21} - 153088 q^{22} - 4228158 q^{23} - 1245184 q^{24} - 1006184 q^{25} - 1287168 q^{26} + 27125676 q^{27} + 3433984 q^{28} - 18298248 q^{29} - 11555072 q^{30} - 16032506 q^{31} - 7030126 q^{33} + 10477568 q^{34} + 43226526 q^{35} + 12371968 q^{36} - 48102882 q^{37} - 25578240 q^{38} + 41142796 q^{39} + 1441792 q^{40} + 68514696 q^{41} + 56269824 q^{42} - 119759664 q^{43} + 2532864 q^{44} - 123651196 q^{45} - 4901632 q^{46} - 4311750 q^{47} + 21233664 q^{48} + 166062156 q^{49} - 23070720 q^{50} + 22294346 q^{51} - 29846528 q^{52} + 90095286 q^{53} - 124568320 q^{54} - 79122004 q^{55} + 48365568 q^{56} - 72348492 q^{57} + 62989312 q^{58} + 131270238 q^{59} - 4107776 q^{60} + 120684718 q^{61} - 87151104 q^{62} - 322269828 q^{63} + 201326592 q^{64} + 147371532 q^{65} + 232417280 q^{66} - 310179826 q^{67} - 73191936 q^{68} - 676075180 q^{69} - 696419584 q^{70} + 865095936 q^{71} - 24379392 q^{72} + 865220822 q^{73} + 56431104 q^{74} + 918577000 q^{75} - 431440896 q^{76} - 1256544870 q^{77} + 1114843136 q^{78} + 483940594 q^{79} - 119144448 q^{80} - 1278021686 q^{81} - 541421568 q^{82} + 146819472 q^{83} - 1059650048 q^{84} - 1566640036 q^{85} + 1052295168 q^{86} + 2165628028 q^{87} + 19595264 q^{88} - 95513418 q^{89} + 1566402560 q^{90} + 1043977168 q^{91} + 2164816896 q^{92} - 1011059438 q^{93} - 1617508608 q^{94} + 912055566 q^{95} - 318767104 q^{96} - 3896128312 q^{97} - 2783840256 q^{98} - 3863644136 q^{99} + O(q^{100})$$

## Decomposition of $$S_{10}^{\mathrm{new}}(14, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
14.10.c.a $$6$$ $$7.211$$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None $$-48$$ $$-233$$ $$-733$$ $$5012$$ $$q+(-2^{4}-2^{4}\beta _{2})q^{2}+(78\beta _{2}-\beta _{3})q^{3}+\cdots$$
14.10.c.b $$6$$ $$7.211$$ $$\mathbb{Q}[x]/(x^{6} - \cdots)$$ None $$48$$ $$71$$ $$-1085$$ $$-6796$$ $$q+(2^{4}+2^{4}\beta _{1})q^{2}+(-24\beta _{1}-\beta _{3})q^{3}+\cdots$$

## Decomposition of $$S_{10}^{\mathrm{old}}(14, [\chi])$$ into lower level spaces

$$S_{10}^{\mathrm{old}}(14, [\chi]) \cong$$ $$S_{10}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 2}$$