Properties

Label 23.2.a
Level $23$
Weight $2$
Character orbit 23.a
Rep. character $\chi_{23}(1,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $4$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 23.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(23))\).

Total New Old
Modular forms 3 3 0
Cusp forms 2 2 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.

\(23\)Dim.
\(-\)\(2\)

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 23
23.2.a.a 23.a 1.a $2$ $0.184$ \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)