Properties

Label 59.3.d
Level $59$
Weight $3$
Character orbit 59.d
Rep. character $\chi_{59}(2,\cdot)$
Character field $\Q(\zeta_{58})$
Dimension $252$
Newform subspaces $1$
Sturm bound $15$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 59 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 59.d (of order \(58\) and degree \(28\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 59 \)
Character field: \(\Q(\zeta_{58})\)
Newform subspaces: \( 1 \)
Sturm bound: \(15\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(59, [\chi])\).

Total New Old
Modular forms 308 308 0
Cusp forms 252 252 0
Eisenstein series 56 56 0

Trace form

\( 252q - 29q^{2} - 33q^{3} - 11q^{4} - 21q^{5} - 29q^{6} - 35q^{7} - 29q^{8} - 70q^{9} + O(q^{10}) \) \( 252q - 29q^{2} - 33q^{3} - 11q^{4} - 21q^{5} - 29q^{6} - 35q^{7} - 29q^{8} - 70q^{9} - 29q^{10} - 29q^{11} + 39q^{12} - 29q^{13} - 29q^{14} + 46q^{15} - 123q^{16} + 8q^{17} - 29q^{18} - 69q^{19} - 133q^{20} - 30q^{21} + 53q^{22} - 29q^{23} - 29q^{24} - 46q^{25} - 167q^{26} - 18q^{27} + 113q^{28} - 57q^{29} - 29q^{30} - 29q^{31} - 29q^{32} - 29q^{33} - 29q^{34} + 10q^{35} + 109q^{36} - 29q^{37} - 29q^{38} - 29q^{39} - 29q^{40} + 101q^{41} - 29q^{42} - 29q^{43} - 29q^{44} + 419q^{45} + 775q^{46} + 290q^{47} + 1131q^{48} + 522q^{49} + 899q^{50} + 527q^{51} + 667q^{52} + 49q^{53} + 783q^{54} + 232q^{55} + 435q^{56} + 251q^{57} - 66q^{59} - 602q^{60} - 203q^{61} - 361q^{62} - 614q^{63} - 1183q^{64} - 638q^{65} - 1589q^{66} - 551q^{67} - 683q^{68} - 1305q^{69} - 1421q^{70} - 810q^{71} - 2465q^{72} - 464q^{73} - 1211q^{74} - 160q^{75} - 69q^{76} - 29q^{77} - 901q^{78} - 399q^{79} + 347q^{80} - 14q^{81} - 29q^{82} - 29q^{83} + 819q^{84} - 193q^{85} + 45q^{86} - 210q^{87} - 655q^{88} - 29q^{89} - 29q^{90} - 29q^{91} - 29q^{92} - 29q^{93} + 291q^{94} + 249q^{95} - 29q^{96} - 29q^{97} + 1624q^{98} + 1537q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(59, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
59.3.d.a \(252\) \(1.608\) None \(-29\) \(-33\) \(-21\) \(-35\)