Properties

Label 17.2.a
Level $17$
Weight $2$
Character orbit 17.a
Rep. character $\chi_{17}(1,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
Sturm bound $3$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 17.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(17))\).

Total New Old
Modular forms 2 2 0
Cusp forms 1 1 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.

\(17\)Dim.
\(-\)\(1\)

Trace form

\( q - q^{2} - q^{4} - 2 q^{5} + 4 q^{7} + 3 q^{8} - 3 q^{9} + O(q^{10}) \) \( q - q^{2} - q^{4} - 2 q^{5} + 4 q^{7} + 3 q^{8} - 3 q^{9} + 2 q^{10} - 2 q^{13} - 4 q^{14} - q^{16} + q^{17} + 3 q^{18} - 4 q^{19} + 2 q^{20} + 4 q^{23} - q^{25} + 2 q^{26} - 4 q^{28} + 6 q^{29} + 4 q^{31} - 5 q^{32} - q^{34} - 8 q^{35} + 3 q^{36} - 2 q^{37} + 4 q^{38} - 6 q^{40} - 6 q^{41} + 4 q^{43} + 6 q^{45} - 4 q^{46} + 9 q^{49} + q^{50} + 2 q^{52} + 6 q^{53} + 12 q^{56} - 6 q^{58} - 12 q^{59} - 10 q^{61} - 4 q^{62} - 12 q^{63} + 7 q^{64} + 4 q^{65} + 4 q^{67} - q^{68} + 8 q^{70} - 4 q^{71} - 9 q^{72} - 6 q^{73} + 2 q^{74} + 4 q^{76} + 12 q^{79} + 2 q^{80} + 9 q^{81} + 6 q^{82} - 4 q^{83} - 2 q^{85} - 4 q^{86} + 10 q^{89} - 6 q^{90} - 8 q^{91} - 4 q^{92} + 8 q^{95} + 2 q^{97} - 9 q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 17
17.2.a.a 17.a 1.a $1$ $0.136$ \(\Q\) None \(-1\) \(0\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-2q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots\)