# Properties

 Label 14.4.c Level $14$ Weight $4$ Character orbit 14.c Rep. character $\chi_{14}(9,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $4$ Newform subspaces $2$ Sturm bound $8$ Trace bound $2$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$14 = 2 \cdot 7$$ Weight: $$k$$ $$=$$ $$4$$ 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: $$8$$ Trace bound: $$2$$ Distinguishing $$T_p$$: $$3$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(14, [\chi])$$.

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

## Trace form

 $$4 q + 6 q^{3} - 8 q^{4} + 2 q^{5} - 16 q^{6} - 48 q^{7} + 28 q^{9} + O(q^{10})$$ $$4 q + 6 q^{3} - 8 q^{4} + 2 q^{5} - 16 q^{6} - 48 q^{7} + 28 q^{9} + 32 q^{10} + 22 q^{11} + 24 q^{12} - 8 q^{13} + 104 q^{14} + 76 q^{15} - 32 q^{16} - 110 q^{17} - 48 q^{18} - 142 q^{19} - 16 q^{20} - 2 q^{21} - 368 q^{22} - 62 q^{23} + 32 q^{24} + 120 q^{25} + 272 q^{26} + 396 q^{27} + 120 q^{28} + 440 q^{29} - 104 q^{30} - 98 q^{31} - 250 q^{33} - 32 q^{34} - 434 q^{35} - 224 q^{36} + 242 q^{37} + 264 q^{38} - 284 q^{39} + 128 q^{40} - 1080 q^{41} + 240 q^{42} + 272 q^{43} + 88 q^{44} + 164 q^{45} - 152 q^{46} - 30 q^{47} - 192 q^{48} - 188 q^{49} + 128 q^{50} + 314 q^{51} + 16 q^{52} + 810 q^{53} - 184 q^{54} + 1516 q^{55} - 64 q^{56} - 324 q^{57} - 16 q^{58} - 202 q^{59} - 152 q^{60} + 658 q^{61} - 208 q^{62} + 372 q^{63} + 256 q^{64} - 1092 q^{65} - 640 q^{66} - 858 q^{67} - 440 q^{68} - 676 q^{69} - 392 q^{70} - 1760 q^{71} - 192 q^{72} + 18 q^{73} + 528 q^{74} - 296 q^{75} + 1136 q^{76} + 1694 q^{77} + 1664 q^{78} + 34 q^{79} + 32 q^{80} + 22 q^{81} - 912 q^{82} + 688 q^{83} - 632 q^{84} - 92 q^{85} + 768 q^{86} + 676 q^{87} + 736 q^{88} + 1890 q^{89} + 800 q^{90} + 640 q^{91} + 496 q^{92} + 190 q^{93} - 744 q^{94} - 914 q^{95} + 128 q^{96} - 4248 q^{97} - 2640 q^{98} - 1592 q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(14, [\chi])$$ into newform subspaces

Label Dim $A$ Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
14.4.c.a $2$ $0.826$ $$\Q(\sqrt{-3})$$ None $$-2$$ $$5$$ $$9$$ $$-28$$ $$q+(-2+2\zeta_{6})q^{2}+5\zeta_{6}q^{3}-4\zeta_{6}q^{4}+\cdots$$
14.4.c.b $2$ $0.826$ $$\Q(\sqrt{-3})$$ None $$2$$ $$1$$ $$-7$$ $$-20$$ $$q+(2-2\zeta_{6})q^{2}+\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-7+\cdots)q^{5}+\cdots$$

## Decomposition of $$S_{4}^{\mathrm{old}}(14, [\chi])$$ into lower level spaces

$$S_{4}^{\mathrm{old}}(14, [\chi]) \cong$$ $$S_{4}^{\mathrm{new}}(7, [\chi])$$$$^{\oplus 2}$$