Properties

Label 23.10.a
Level 23
Weight 10
Character orbit a
Rep. character \(\chi_{23}(1,\cdot)\)
Character field \(\Q\)
Dimension 17
Newforms 2
Sturm bound 20
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 10 \)
Character orbit: \([\chi]\) = 23.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(20\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(23))\).

Total New Old
Modular forms 19 17 2
Cusp forms 17 17 0
Eisenstein series 2 0 2

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

\(23\)Dim.
\(+\)\(7\)
\(-\)\(10\)

Trace form

\(17q \) \(\mathstrut +\mathstrut 32q^{2} \) \(\mathstrut +\mathstrut 146q^{3} \) \(\mathstrut +\mathstrut 4608q^{4} \) \(\mathstrut -\mathstrut 2276q^{5} \) \(\mathstrut -\mathstrut 1543q^{6} \) \(\mathstrut -\mathstrut 8616q^{7} \) \(\mathstrut +\mathstrut 28401q^{8} \) \(\mathstrut +\mathstrut 84745q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(17q \) \(\mathstrut +\mathstrut 32q^{2} \) \(\mathstrut +\mathstrut 146q^{3} \) \(\mathstrut +\mathstrut 4608q^{4} \) \(\mathstrut -\mathstrut 2276q^{5} \) \(\mathstrut -\mathstrut 1543q^{6} \) \(\mathstrut -\mathstrut 8616q^{7} \) \(\mathstrut +\mathstrut 28401q^{8} \) \(\mathstrut +\mathstrut 84745q^{9} \) \(\mathstrut +\mathstrut 1474q^{10} \) \(\mathstrut -\mathstrut 81174q^{11} \) \(\mathstrut +\mathstrut 60577q^{12} \) \(\mathstrut +\mathstrut 11078q^{13} \) \(\mathstrut -\mathstrut 67832q^{14} \) \(\mathstrut +\mathstrut 347320q^{15} \) \(\mathstrut +\mathstrut 1430800q^{16} \) \(\mathstrut -\mathstrut 301206q^{17} \) \(\mathstrut +\mathstrut 2246597q^{18} \) \(\mathstrut -\mathstrut 825798q^{19} \) \(\mathstrut -\mathstrut 3392500q^{20} \) \(\mathstrut +\mathstrut 2109124q^{21} \) \(\mathstrut +\mathstrut 792988q^{22} \) \(\mathstrut +\mathstrut 839523q^{23} \) \(\mathstrut +\mathstrut 1989844q^{24} \) \(\mathstrut +\mathstrut 7754339q^{25} \) \(\mathstrut -\mathstrut 758787q^{26} \) \(\mathstrut +\mathstrut 5020046q^{27} \) \(\mathstrut -\mathstrut 15942102q^{28} \) \(\mathstrut -\mathstrut 3198222q^{29} \) \(\mathstrut +\mathstrut 175166q^{30} \) \(\mathstrut -\mathstrut 1294090q^{31} \) \(\mathstrut +\mathstrut 610344q^{32} \) \(\mathstrut -\mathstrut 20898996q^{33} \) \(\mathstrut +\mathstrut 4616162q^{34} \) \(\mathstrut -\mathstrut 10749904q^{35} \) \(\mathstrut +\mathstrut 8658387q^{36} \) \(\mathstrut -\mathstrut 18252572q^{37} \) \(\mathstrut +\mathstrut 2049956q^{38} \) \(\mathstrut -\mathstrut 26458230q^{39} \) \(\mathstrut -\mathstrut 58981690q^{40} \) \(\mathstrut +\mathstrut 10514474q^{41} \) \(\mathstrut +\mathstrut 112029344q^{42} \) \(\mathstrut -\mathstrut 7369558q^{43} \) \(\mathstrut -\mathstrut 119503186q^{44} \) \(\mathstrut -\mathstrut 72424656q^{45} \) \(\mathstrut +\mathstrut 8954912q^{46} \) \(\mathstrut +\mathstrut 98827686q^{47} \) \(\mathstrut -\mathstrut 142621097q^{48} \) \(\mathstrut +\mathstrut 146632153q^{49} \) \(\mathstrut +\mathstrut 145540120q^{50} \) \(\mathstrut +\mathstrut 63418908q^{51} \) \(\mathstrut +\mathstrut 148826435q^{52} \) \(\mathstrut +\mathstrut 120705064q^{53} \) \(\mathstrut +\mathstrut 35622927q^{54} \) \(\mathstrut +\mathstrut 282856200q^{55} \) \(\mathstrut -\mathstrut 178949470q^{56} \) \(\mathstrut -\mathstrut 25645736q^{57} \) \(\mathstrut -\mathstrut 33356229q^{58} \) \(\mathstrut -\mathstrut 247124084q^{59} \) \(\mathstrut +\mathstrut 208400484q^{60} \) \(\mathstrut -\mathstrut 102318260q^{61} \) \(\mathstrut +\mathstrut 184772901q^{62} \) \(\mathstrut -\mathstrut 178441268q^{63} \) \(\mathstrut +\mathstrut 64026955q^{64} \) \(\mathstrut +\mathstrut 339027084q^{65} \) \(\mathstrut -\mathstrut 1024843498q^{66} \) \(\mathstrut -\mathstrut 58802426q^{67} \) \(\mathstrut -\mathstrut 129158932q^{68} \) \(\mathstrut +\mathstrut 90668484q^{69} \) \(\mathstrut -\mathstrut 554208476q^{70} \) \(\mathstrut -\mathstrut 40561570q^{71} \) \(\mathstrut +\mathstrut 1534141671q^{72} \) \(\mathstrut -\mathstrut 256576838q^{73} \) \(\mathstrut -\mathstrut 1126353786q^{74} \) \(\mathstrut +\mathstrut 609060646q^{75} \) \(\mathstrut -\mathstrut 1537770376q^{76} \) \(\mathstrut +\mathstrut 1171153664q^{77} \) \(\mathstrut +\mathstrut 371613403q^{78} \) \(\mathstrut +\mathstrut 663186704q^{79} \) \(\mathstrut -\mathstrut 2996015778q^{80} \) \(\mathstrut -\mathstrut 97664023q^{81} \) \(\mathstrut -\mathstrut 1564524883q^{82} \) \(\mathstrut +\mathstrut 2618284202q^{83} \) \(\mathstrut +\mathstrut 3474690006q^{84} \) \(\mathstrut +\mathstrut 759665864q^{85} \) \(\mathstrut -\mathstrut 791477334q^{86} \) \(\mathstrut -\mathstrut 1045322842q^{87} \) \(\mathstrut +\mathstrut 1112258828q^{88} \) \(\mathstrut -\mathstrut 1013790702q^{89} \) \(\mathstrut -\mathstrut 4913217940q^{90} \) \(\mathstrut -\mathstrut 2183938212q^{91} \) \(\mathstrut +\mathstrut 429835776q^{92} \) \(\mathstrut -\mathstrut 1793259136q^{93} \) \(\mathstrut -\mathstrut 1407723175q^{94} \) \(\mathstrut +\mathstrut 4158946840q^{95} \) \(\mathstrut -\mathstrut 1847006745q^{96} \) \(\mathstrut +\mathstrut 1242886026q^{97} \) \(\mathstrut +\mathstrut 6221282828q^{98} \) \(\mathstrut -\mathstrut 1409015358q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(23))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 23
23.10.a.a \(7\) \(11.846\) \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(0\) \(-89\) \(-2388\) \(-9896\) \(+\) \(q+\beta _{1}q^{2}+(-13-2\beta _{1}-\beta _{4})q^{3}+(220+\cdots)q^{4}+\cdots\)
23.10.a.b \(10\) \(11.846\) \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(32\) \(235\) \(112\) \(1280\) \(-\) \(q+(3+\beta _{1})q^{2}+(23+\beta _{1}+\beta _{3})q^{3}+(307+\cdots)q^{4}+\cdots\)