Properties

Label 23.8.a
Level 23
Weight 8
Character orbit a
Rep. character \(\chi_{23}(1,\cdot)\)
Character field \(\Q\)
Dimension 13
Newforms 2
Sturm bound 16
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 23.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(16\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(23))\).

Total New Old
Modular forms 15 13 2
Cusp forms 13 13 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.
\(+\)\(8\)
\(-\)\(5\)

Trace form

\(13q \) \(\mathstrut -\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 28q^{3} \) \(\mathstrut +\mathstrut 896q^{4} \) \(\mathstrut +\mathstrut 388q^{5} \) \(\mathstrut -\mathstrut 1207q^{6} \) \(\mathstrut +\mathstrut 290q^{7} \) \(\mathstrut -\mathstrut 2775q^{8} \) \(\mathstrut +\mathstrut 11683q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 16q^{2} \) \(\mathstrut -\mathstrut 28q^{3} \) \(\mathstrut +\mathstrut 896q^{4} \) \(\mathstrut +\mathstrut 388q^{5} \) \(\mathstrut -\mathstrut 1207q^{6} \) \(\mathstrut +\mathstrut 290q^{7} \) \(\mathstrut -\mathstrut 2775q^{8} \) \(\mathstrut +\mathstrut 11683q^{9} \) \(\mathstrut +\mathstrut 8242q^{10} \) \(\mathstrut +\mathstrut 6270q^{11} \) \(\mathstrut -\mathstrut 5279q^{12} \) \(\mathstrut +\mathstrut 200q^{13} \) \(\mathstrut +\mathstrut 10696q^{14} \) \(\mathstrut -\mathstrut 37370q^{15} \) \(\mathstrut +\mathstrut 96784q^{16} \) \(\mathstrut +\mathstrut 37068q^{17} \) \(\mathstrut -\mathstrut 83779q^{18} \) \(\mathstrut -\mathstrut 37264q^{19} \) \(\mathstrut +\mathstrut 107804q^{20} \) \(\mathstrut +\mathstrut 25582q^{21} \) \(\mathstrut -\mathstrut 203092q^{22} \) \(\mathstrut -\mathstrut 36501q^{23} \) \(\mathstrut -\mathstrut 259196q^{24} \) \(\mathstrut +\mathstrut 104455q^{25} \) \(\mathstrut -\mathstrut 26331q^{26} \) \(\mathstrut +\mathstrut 31400q^{27} \) \(\mathstrut +\mathstrut 233850q^{28} \) \(\mathstrut -\mathstrut 253212q^{29} \) \(\mathstrut -\mathstrut 155746q^{30} \) \(\mathstrut +\mathstrut 124232q^{31} \) \(\mathstrut -\mathstrut 1016856q^{32} \) \(\mathstrut +\mathstrut 127554q^{33} \) \(\mathstrut -\mathstrut 492414q^{34} \) \(\mathstrut +\mathstrut 157016q^{35} \) \(\mathstrut +\mathstrut 2379507q^{36} \) \(\mathstrut -\mathstrut 466200q^{37} \) \(\mathstrut -\mathstrut 306124q^{38} \) \(\mathstrut +\mathstrut 824832q^{39} \) \(\mathstrut +\mathstrut 1022710q^{40} \) \(\mathstrut +\mathstrut 131504q^{41} \) \(\mathstrut -\mathstrut 2136688q^{42} \) \(\mathstrut +\mathstrut 1119932q^{43} \) \(\mathstrut +\mathstrut 1599806q^{44} \) \(\mathstrut +\mathstrut 1697490q^{45} \) \(\mathstrut -\mathstrut 194672q^{46} \) \(\mathstrut -\mathstrut 332904q^{47} \) \(\mathstrut -\mathstrut 505313q^{48} \) \(\mathstrut -\mathstrut 2060623q^{49} \) \(\mathstrut +\mathstrut 3029752q^{50} \) \(\mathstrut +\mathstrut 2563962q^{51} \) \(\mathstrut -\mathstrut 3435925q^{52} \) \(\mathstrut +\mathstrut 1100758q^{53} \) \(\mathstrut -\mathstrut 8052873q^{54} \) \(\mathstrut +\mathstrut 178724q^{55} \) \(\mathstrut -\mathstrut 2716702q^{56} \) \(\mathstrut +\mathstrut 7045840q^{57} \) \(\mathstrut +\mathstrut 645099q^{58} \) \(\mathstrut +\mathstrut 272080q^{59} \) \(\mathstrut -\mathstrut 19632684q^{60} \) \(\mathstrut -\mathstrut 2696542q^{61} \) \(\mathstrut -\mathstrut 2277483q^{62} \) \(\mathstrut +\mathstrut 2546764q^{63} \) \(\mathstrut +\mathstrut 7875515q^{64} \) \(\mathstrut -\mathstrut 2922090q^{65} \) \(\mathstrut +\mathstrut 15485078q^{66} \) \(\mathstrut +\mathstrut 1712466q^{67} \) \(\mathstrut +\mathstrut 7416284q^{68} \) \(\mathstrut -\mathstrut 1314036q^{69} \) \(\mathstrut +\mathstrut 8077524q^{70} \) \(\mathstrut -\mathstrut 1906780q^{71} \) \(\mathstrut -\mathstrut 14681145q^{72} \) \(\mathstrut +\mathstrut 2147348q^{73} \) \(\mathstrut +\mathstrut 1765446q^{74} \) \(\mathstrut -\mathstrut 11646944q^{75} \) \(\mathstrut +\mathstrut 4009288q^{76} \) \(\mathstrut -\mathstrut 8786560q^{77} \) \(\mathstrut -\mathstrut 16787141q^{78} \) \(\mathstrut -\mathstrut 235076q^{79} \) \(\mathstrut +\mathstrut 20983422q^{80} \) \(\mathstrut +\mathstrut 2298893q^{81} \) \(\mathstrut +\mathstrut 24898605q^{82} \) \(\mathstrut -\mathstrut 4118794q^{83} \) \(\mathstrut +\mathstrut 10292934q^{84} \) \(\mathstrut +\mathstrut 1228492q^{85} \) \(\mathstrut -\mathstrut 17707254q^{86} \) \(\mathstrut +\mathstrut 22013600q^{87} \) \(\mathstrut -\mathstrut 21225300q^{88} \) \(\mathstrut +\mathstrut 10585266q^{89} \) \(\mathstrut +\mathstrut 44050700q^{90} \) \(\mathstrut +\mathstrut 5729214q^{91} \) \(\mathstrut -\mathstrut 4672128q^{92} \) \(\mathstrut -\mathstrut 16182766q^{93} \) \(\mathstrut -\mathstrut 1579647q^{94} \) \(\mathstrut -\mathstrut 28722596q^{95} \) \(\mathstrut -\mathstrut 4620465q^{96} \) \(\mathstrut +\mathstrut 12189100q^{97} \) \(\mathstrut +\mathstrut 22688396q^{98} \) \(\mathstrut -\mathstrut 34528176q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(23))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 23
23.8.a.a \(5\) \(7.185\) \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(-16\) \(-68\) \(-56\) \(-1156\) \(-\) \(q+(-3+\beta _{1})q^{2}+(-14+\beta _{2})q^{3}+(51+\cdots)q^{4}+\cdots\)
23.8.a.b \(8\) \(7.185\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(40\) \(444\) \(1446\) \(+\) \(q+\beta _{1}q^{2}+(5-\beta _{1}+\beta _{2})q^{3}+(80+2\beta _{1}+\cdots)q^{4}+\cdots\)