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Properties

Label 67.2.e
Level $67$
Weight $2$
Character orbit 67.e
Rep. character $\chi_{67}(9,\cdot)$
Character field $\Q(\zeta_{11})$
Dimension $40$
Newform subspaces $3$
Sturm bound $11$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 67 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 67.e (of order \(11\) and degree \(10\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 67 \)
Character field: \(\Q(\zeta_{11})\)
Newform subspaces: \( 3 \)
Sturm bound: \(11\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 60 60 0
Cusp forms 40 40 0
Eisenstein series 20 20 0

Trace form

\( 40 q - 6 q^{2} - 3 q^{3} - 8 q^{4} - 5 q^{5} + q^{6} - q^{7} - 23 q^{8} + 3 q^{9} + O(q^{10}) \) \( 40 q - 6 q^{2} - 3 q^{3} - 8 q^{4} - 5 q^{5} + q^{6} - q^{7} - 23 q^{8} + 3 q^{9} - 32 q^{10} + 3 q^{11} - 12 q^{12} + 9 q^{13} + 11 q^{14} - 11 q^{15} + 14 q^{16} - 29 q^{17} + 16 q^{18} - 10 q^{19} + 33 q^{20} - 41 q^{21} - 16 q^{22} - 11 q^{23} - 11 q^{24} + 5 q^{25} + 21 q^{26} + 27 q^{27} + 16 q^{28} - 2 q^{29} + 16 q^{30} - 11 q^{31} + 11 q^{32} + 12 q^{33} + 41 q^{34} + 31 q^{35} + 45 q^{36} + 4 q^{37} - 56 q^{38} - 37 q^{39} - 4 q^{40} - 4 q^{41} + 77 q^{42} - 3 q^{43} + 67 q^{44} - 31 q^{45} - 4 q^{46} + 27 q^{47} + q^{48} + 51 q^{49} - 56 q^{50} + 55 q^{51} - 81 q^{52} + 40 q^{53} - 61 q^{54} + 10 q^{55} - 17 q^{56} - 15 q^{57} - q^{58} - 81 q^{59} + 65 q^{60} - 63 q^{61} + 65 q^{62} - 44 q^{63} - 27 q^{64} + 11 q^{65} - 138 q^{66} + 33 q^{67} - 196 q^{68} + 71 q^{69} - 41 q^{70} + 5 q^{71} - 58 q^{72} - 70 q^{73} + 51 q^{74} - 70 q^{75} + 23 q^{76} - 85 q^{77} + 129 q^{78} - 48 q^{79} + 67 q^{80} + 44 q^{81} - 40 q^{82} + 49 q^{83} - 15 q^{84} + 51 q^{85} - 75 q^{86} - 14 q^{87} + 57 q^{88} + 55 q^{89} + 21 q^{90} - 5 q^{91} + 65 q^{92} - 75 q^{93} + 65 q^{94} + 92 q^{95} - 6 q^{96} + 30 q^{97} + 140 q^{98} + 112 q^{99} + O(q^{100}) \)

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.e.a 67.e 67.e $10$ $0.535$ \(\Q(\zeta_{22})\) None \(-6\) \(-2\) \(3\) \(0\) $\mathrm{SU}(2)[C_{11}]$ \(q+(-1-\zeta_{22}^{2}-\zeta_{22}^{4}+\zeta_{22}^{7}-\zeta_{22}^{8}+\cdots)q^{2}+\cdots\)
67.2.e.b 67.e 67.e $10$ $0.535$ \(\Q(\zeta_{22})\) None \(4\) \(3\) \(-9\) \(7\) $\mathrm{SU}(2)[C_{11}]$ \(q+(1-\zeta_{22}+\zeta_{22}^{2}-\zeta_{22}^{3}+\zeta_{22}^{4}+\cdots)q^{2}+\cdots\)
67.2.e.c 67.e 67.e $20$ $0.535$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-4\) \(-4\) \(1\) \(-8\) $\mathrm{SU}(2)[C_{11}]$ \(q+(-\beta _{9}-\beta _{14})q^{2}-\beta _{19}q^{3}+(-1+\cdots)q^{4}+\cdots\)