↑

Properties

Label 109.2.a
Level $109$
Weight $2$
Character orbit 109.a
Rep. character $\chi_{109}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $3$
Sturm bound $18$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 109 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 109.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(18\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(109))\).

Total New Old
Modular forms 9 9 0
Cusp forms 8 8 0
Eisenstein series 1 1 0

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(109\)Dim
\(+\)\(3\)
\(-\)\(5\)

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(109))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 109
109.2.a.a 109.a 1.a $1$ $0.870$ \(\Q\) None \(1\) \(0\) \(3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{4}+3q^{5}+2q^{7}-3q^{8}-3q^{9}+\cdots\)
109.2.a.b 109.a 1.a $3$ $0.870$ \(\Q(\zeta_{14})^+\) None \(-2\) \(-4\) \(-6\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{2})q^{2}+(-1+\beta _{2})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
109.2.a.c 109.a 1.a $4$ $0.870$ 4.4.7537.1 None \(-1\) \(4\) \(1\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)