# Properties

 Label 43.4.c Level $43$ Weight $4$ Character orbit 43.c Rep. character $\chi_{43}(6,\cdot)$ Character field $\Q(\zeta_{3})$ Dimension $20$ Newform subspaces $1$ Sturm bound $14$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$43$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 43.c (of order $$3$$ and degree $$2$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$43$$ Character field: $$\Q(\zeta_{3})$$ Newform subspaces: $$1$$ Sturm bound: $$14$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{4}(43, [\chi])$$.

Total New Old
Modular forms 24 24 0
Cusp forms 20 20 0
Eisenstein series 4 4 0

## Trace form

 $$20q - 2q^{2} - 5q^{3} + 78q^{4} - 19q^{5} + 15q^{6} - 51q^{7} - 72q^{8} - 117q^{9} + O(q^{10})$$ $$20q - 2q^{2} - 5q^{3} + 78q^{4} - 19q^{5} + 15q^{6} - 51q^{7} - 72q^{8} - 117q^{9} + 27q^{10} + 54q^{11} - 72q^{12} - 15q^{13} + 96q^{14} + 65q^{15} + 134q^{16} - 82q^{17} + 247q^{18} + 78q^{19} - 495q^{20} - 18q^{21} + 380q^{22} - 61q^{23} + 202q^{24} - 151q^{25} - 21q^{26} - 194q^{27} - 794q^{28} - 53q^{29} + 627q^{30} + 253q^{31} - 798q^{32} - 424q^{33} - 231q^{34} + 710q^{35} - 1092q^{36} - 129q^{37} - 854q^{38} + 1382q^{39} + 1345q^{40} + 782q^{41} + 62q^{42} + 1025q^{43} + 754q^{44} + 1888q^{45} - 40q^{46} - 668q^{47} - 2401q^{48} - 115q^{49} + 424q^{50} + 1590q^{51} - 564q^{52} + 773q^{53} + 364q^{54} - 1242q^{55} - 923q^{56} - 765q^{57} + 1328q^{58} - 2966q^{59} - 1075q^{60} + 437q^{61} + 1509q^{62} - 2222q^{63} - 1476q^{64} - 2126q^{65} + 1483q^{66} - 642q^{67} - 1052q^{68} - 3503q^{69} - 170q^{70} - 1545q^{71} + 3834q^{72} + 1292q^{73} - 2232q^{74} + 164q^{75} - 252q^{76} + 1448q^{77} + 5644q^{78} - 1405q^{79} - 3157q^{80} + 974q^{81} + 6608q^{82} + 543q^{83} + 7304q^{84} + 1946q^{85} + 2776q^{86} + 2818q^{87} - 5372q^{88} - 2196q^{89} - 1484q^{90} - 3513q^{91} + 2629q^{92} - 983q^{93} + 9878q^{94} - 149q^{95} + 3540q^{96} - 850q^{97} - 213q^{98} - 3181q^{99} + O(q^{100})$$

## Decomposition of $$S_{4}^{\mathrm{new}}(43, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
43.4.c.a $$20$$ $$2.537$$ $$\mathbb{Q}[x]/(x^{20} - \cdots)$$ None $$-2$$ $$-5$$ $$-19$$ $$-51$$ $$q+\beta _{5}q^{2}+(-\beta _{4}-\beta _{6})q^{3}+(4+\beta _{2}+\cdots)q^{4}+\cdots$$