Properties

Label 109.2.e
Level $109$
Weight $2$
Character orbit 109.e
Rep. character $\chi_{109}(46,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $2$
Sturm bound $18$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 109 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 109.e (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 109 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(18\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(109, [\chi])\).

Total New Old
Modular forms 20 20 0
Cusp forms 16 16 0
Eisenstein series 4 4 0

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(109, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
109.2.e.a 109.e 109.e $2$ $0.870$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-3\) \(1\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+2\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-q^{4}+\cdots\)
109.2.e.b 109.e 109.e $14$ $0.870$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(-4\) \(-2\) \(-7\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{1}q^{2}+(\beta _{5}+\beta _{10}-\beta _{13})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)