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 $0$

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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 \(-26\) \(-23\) \(-25\) \(-23\)