# Properties

 Label 59.2.c Level $59$ Weight $2$ Character orbit 59.c Rep. character $\chi_{59}(3,\cdot)$ Character field $\Q(\zeta_{29})$ Dimension $112$ Newform subspaces $1$ Sturm bound $10$ Trace bound $0$

# Related objects

## Defining parameters

 Level: $$N$$ $$=$$ $$59$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 59.c (of order $$29$$ and degree $$28$$) Character conductor: $$\operatorname{cond}(\chi)$$ $$=$$ $$59$$ Character field: $$\Q(\zeta_{29})$$ Newform subspaces: $$1$$ Sturm bound: $$10$$ Trace bound: $$0$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(59, [\chi])$$.

Total New Old
Modular forms 168 168 0
Cusp forms 112 112 0
Eisenstein series 56 56 0

## Trace form

 $$112q - 26q^{2} - 23q^{3} - 30q^{4} - 25q^{5} - 13q^{6} - 23q^{7} - 8q^{8} - 21q^{9} + O(q^{10})$$ $$112q - 26q^{2} - 23q^{3} - 30q^{4} - 25q^{5} - 13q^{6} - 23q^{7} - 8q^{8} - 21q^{9} - 3q^{10} - 15q^{11} + 21q^{12} - 23q^{13} + 13q^{14} + 4q^{15} - 8q^{16} - 10q^{17} + 12q^{18} - 15q^{19} + 7q^{20} - 12q^{21} - q^{22} + 3q^{23} + 25q^{24} - 5q^{25} + 5q^{26} + 22q^{27} + 29q^{28} - 13q^{29} + 29q^{30} + 3q^{31} + 36q^{32} + 33q^{33} + 27q^{34} + 28q^{35} + 20q^{36} - 9q^{37} + 31q^{38} + 45q^{39} + 79q^{40} + 23q^{41} + 33q^{42} + 19q^{43} + 43q^{44} + 19q^{45} - 31q^{46} + 10q^{47} - 25q^{48} - 31q^{49} - 60q^{50} - 61q^{51} - 75q^{52} - 23q^{53} - 86q^{54} - 24q^{55} - 103q^{56} - 91q^{57} + 12q^{58} - 33q^{59} - 210q^{60} - 47q^{61} - 39q^{62} - 58q^{63} - 152q^{64} - 16q^{65} - 116q^{66} - 19q^{67} - 5q^{68} - 45q^{69} + 23q^{70} - 18q^{71} - 36q^{72} + 24q^{73} + 19q^{74} + 58q^{75} + 97q^{76} + 65q^{77} + 119q^{78} + 41q^{79} + 107q^{80} + 95q^{81} + 145q^{82} + 49q^{83} + 167q^{84} + 39q^{85} + 111q^{86} + 80q^{87} + 175q^{88} + 51q^{89} + 213q^{90} + 77q^{91} + 135q^{92} + 93q^{93} + 151q^{94} + 65q^{95} + 181q^{96} + 91q^{97} + 31q^{98} + 44q^{99} + O(q^{100})$$

## Decomposition of $$S_{2}^{\mathrm{new}}(59, [\chi])$$ into newform subspaces

Label Dim. $$A$$ Field CM Traces $q$-expansion
$$a_2$$ $$a_3$$ $$a_5$$ $$a_7$$
59.2.c.a $$112$$ $$0.471$$ None $$-26$$ $$-23$$ $$-25$$ $$-23$$