↑

Properties

Label 171.2.e
Level $171$
Weight $2$
Character orbit 171.e
Rep. character $\chi_{171}(58,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $36$
Newform subspaces $2$
Sturm bound $40$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 171 = 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 171.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(40\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(171, [\chi])\).

Total New Old
Modular forms 44 36 8
Cusp forms 36 36 0
Eisenstein series 8 0 8

Trace form

\( 36 q - 2 q^{3} - 18 q^{4} - 2 q^{5} + 2 q^{6} - 12 q^{8} + 2 q^{9} + O(q^{10}) \) \( 36 q - 2 q^{3} - 18 q^{4} - 2 q^{5} + 2 q^{6} - 12 q^{8} + 2 q^{9} - 4 q^{11} - 6 q^{12} + 14 q^{14} - 8 q^{15} - 18 q^{16} + 16 q^{17} - 24 q^{18} - 4 q^{20} - 10 q^{21} - 10 q^{23} + 24 q^{24} - 12 q^{25} + 16 q^{26} - 14 q^{27} + 4 q^{29} + 16 q^{30} + 6 q^{31} + 12 q^{32} - 2 q^{33} - 12 q^{35} - 10 q^{36} - 12 q^{37} - 6 q^{38} + 30 q^{39} - 8 q^{41} + 34 q^{42} + 40 q^{44} - 8 q^{45} - 24 q^{46} - 6 q^{47} - 6 q^{48} - 6 q^{49} - 14 q^{50} - 40 q^{51} + 18 q^{52} - 16 q^{53} + 20 q^{54} + 12 q^{55} + 60 q^{56} + 6 q^{58} + 14 q^{59} - 10 q^{60} + 12 q^{61} - 64 q^{62} + 48 q^{63} + 18 q^{65} + 70 q^{66} + 6 q^{67} - 40 q^{68} - 84 q^{71} - 72 q^{72} - 70 q^{74} + 20 q^{75} + 14 q^{77} + 56 q^{78} + 44 q^{80} - 46 q^{81} + 12 q^{82} - 8 q^{83} + 66 q^{84} - 12 q^{85} - 24 q^{86} - 36 q^{87} - 24 q^{88} - 56 q^{89} + 10 q^{90} - 24 q^{91} + 22 q^{92} - 30 q^{93} + 6 q^{94} - 16 q^{95} - 68 q^{96} - 18 q^{97} + 152 q^{98} + 44 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(171, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
171.2.e.a 171.e 9.c $18$ $1.365$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(-3\) \(-1\) \(-9\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{4})q^{2}+(\beta _{2}+\beta _{10})q^{3}+(-\beta _{2}+\cdots)q^{4}+\cdots\)
171.2.e.b 171.e 9.c $18$ $1.365$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None \(3\) \(-1\) \(7\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{8}+\beta _{11})q^{2}+(-\beta _{3}+\beta _{16})q^{3}+\cdots\)