↑

Properties

Label 67.2.c
Level $67$
Weight $2$
Character orbit 67.c
Rep. character $\chi_{67}(29,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $10$
Newform subspaces $1$
Sturm bound $11$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 67.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 67 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(11\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(67, [\chi])\).

Total New Old
Modular forms 14 14 0
Cusp forms 10 10 0
Eisenstein series 4 4 0

Trace form

\( 10 q + 2 q^{2} - 8 q^{3} - 4 q^{4} - 6 q^{5} - 6 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9} + O(q^{10}) \) \( 10 q + 2 q^{2} - 8 q^{3} - 4 q^{4} - 6 q^{5} - 6 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9} + 3 q^{10} + 2 q^{11} + 7 q^{12} + 10 q^{14} - 2 q^{15} + 6 q^{16} - 6 q^{17} + 6 q^{18} - 7 q^{20} - 2 q^{21} - 16 q^{22} + 2 q^{23} + 42 q^{24} + 12 q^{25} + 5 q^{26} - 50 q^{27} + 11 q^{28} - 8 q^{29} - 35 q^{30} + 12 q^{31} - q^{32} - 14 q^{33} + 28 q^{34} - 21 q^{35} - 22 q^{36} - 7 q^{37} + 5 q^{38} + 17 q^{39} - 10 q^{40} + 16 q^{41} + 16 q^{42} + 20 q^{43} - 3 q^{44} + 18 q^{45} - 19 q^{46} + 17 q^{47} + 16 q^{48} + 5 q^{49} + 20 q^{50} - 32 q^{52} + 8 q^{53} - 18 q^{54} - 2 q^{55} - 8 q^{56} + 14 q^{57} - 32 q^{58} + 6 q^{59} + 42 q^{60} - 6 q^{61} + 8 q^{62} + 8 q^{63} - 12 q^{64} - 18 q^{65} + 6 q^{66} - 10 q^{67} + 94 q^{68} + 23 q^{69} - 44 q^{70} + 3 q^{71} - 106 q^{72} - 34 q^{73} - 20 q^{74} - 46 q^{75} - 32 q^{76} + 3 q^{77} - 2 q^{78} + 8 q^{79} - 31 q^{80} + 50 q^{81} + 42 q^{82} + 28 q^{83} + 3 q^{84} - 16 q^{85} + 9 q^{86} + 27 q^{87} - 19 q^{88} - 84 q^{89} + 77 q^{90} + 68 q^{91} + 18 q^{92} + q^{93} - 48 q^{94} + 31 q^{95} + 19 q^{96} - 20 q^{97} + 21 q^{98} + 31 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(67, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
67.2.c.a 67.c 67.c $10$ $0.535$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(2\) \(-8\) \(-6\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{5})q^{2}+(-1+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)