Properties

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

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 23.a (trivial)
Character field: \(\Q\)
Newforms: \( 1 \)
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.

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

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 23
23.2.a.a \(2\) \(0.184\) \(\Q(\sqrt{5}) \) None \(-1\) \(0\) \(-2\) \(2\) \(-\) \(q-\beta q^{2}+(-1+2\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)