Properties

Label 23.4.a
Level 23
Weight 4
Character orbit a
Rep. character \(\chi_{23}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 2
Sturm bound 8
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 23.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(23))\).

Total New Old
Modular forms 7 5 2
Cusp forms 5 5 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.
\(+\)\(4\)
\(-\)\(1\)

Trace form

\(5q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut -\mathstrut 35q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut +\mathstrut 2q^{3} \) \(\mathstrut +\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 8q^{5} \) \(\mathstrut -\mathstrut 7q^{6} \) \(\mathstrut +\mathstrut 8q^{7} \) \(\mathstrut -\mathstrut 39q^{8} \) \(\mathstrut -\mathstrut 35q^{9} \) \(\mathstrut -\mathstrut 58q^{10} \) \(\mathstrut +\mathstrut 42q^{11} \) \(\mathstrut -\mathstrut 47q^{12} \) \(\mathstrut +\mathstrut 54q^{13} \) \(\mathstrut -\mathstrut 128q^{14} \) \(\mathstrut +\mathstrut 40q^{15} \) \(\mathstrut +\mathstrut 48q^{16} \) \(\mathstrut +\mathstrut 18q^{17} \) \(\mathstrut +\mathstrut 53q^{18} \) \(\mathstrut +\mathstrut 26q^{19} \) \(\mathstrut +\mathstrut 164q^{20} \) \(\mathstrut +\mathstrut 220q^{21} \) \(\mathstrut +\mathstrut 152q^{22} \) \(\mathstrut -\mathstrut 69q^{23} \) \(\mathstrut -\mathstrut 308q^{24} \) \(\mathstrut +\mathstrut 95q^{25} \) \(\mathstrut -\mathstrut 115q^{26} \) \(\mathstrut -\mathstrut 10q^{27} \) \(\mathstrut +\mathstrut 314q^{28} \) \(\mathstrut +\mathstrut 266q^{29} \) \(\mathstrut -\mathstrut 466q^{30} \) \(\mathstrut -\mathstrut 90q^{31} \) \(\mathstrut -\mathstrut 592q^{32} \) \(\mathstrut -\mathstrut 588q^{33} \) \(\mathstrut +\mathstrut 826q^{34} \) \(\mathstrut -\mathstrut 704q^{35} \) \(\mathstrut -\mathstrut 621q^{36} \) \(\mathstrut -\mathstrut 128q^{37} \) \(\mathstrut +\mathstrut 888q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 170q^{40} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 560q^{42} \) \(\mathstrut +\mathstrut 90q^{43} \) \(\mathstrut +\mathstrut 694q^{44} \) \(\mathstrut +\mathstrut 180q^{45} \) \(\mathstrut -\mathstrut 92q^{46} \) \(\mathstrut -\mathstrut 1034q^{47} \) \(\mathstrut +\mathstrut 631q^{48} \) \(\mathstrut +\mathstrut 941q^{49} \) \(\mathstrut +\mathstrut 592q^{50} \) \(\mathstrut +\mathstrut 60q^{51} \) \(\mathstrut +\mathstrut 2475q^{52} \) \(\mathstrut -\mathstrut 644q^{53} \) \(\mathstrut +\mathstrut 351q^{54} \) \(\mathstrut -\mathstrut 1176q^{55} \) \(\mathstrut -\mathstrut 2366q^{56} \) \(\mathstrut +\mathstrut 1672q^{57} \) \(\mathstrut -\mathstrut 2325q^{58} \) \(\mathstrut -\mathstrut 1548q^{59} \) \(\mathstrut -\mathstrut 924q^{60} \) \(\mathstrut +\mathstrut 1576q^{61} \) \(\mathstrut +\mathstrut 237q^{62} \) \(\mathstrut -\mathstrut 1076q^{63} \) \(\mathstrut -\mathstrut 357q^{64} \) \(\mathstrut +\mathstrut 1660q^{65} \) \(\mathstrut -\mathstrut 58q^{66} \) \(\mathstrut +\mathstrut 1414q^{67} \) \(\mathstrut +\mathstrut 604q^{68} \) \(\mathstrut -\mathstrut 276q^{69} \) \(\mathstrut -\mathstrut 3916q^{70} \) \(\mathstrut -\mathstrut 66q^{71} \) \(\mathstrut +\mathstrut 1455q^{72} \) \(\mathstrut +\mathstrut 610q^{73} \) \(\mathstrut +\mathstrut 1962q^{74} \) \(\mathstrut +\mathstrut 1846q^{75} \) \(\mathstrut -\mathstrut 3552q^{76} \) \(\mathstrut +\mathstrut 464q^{77} \) \(\mathstrut -\mathstrut 2477q^{78} \) \(\mathstrut -\mathstrut 2160q^{79} \) \(\mathstrut +\mathstrut 2942q^{80} \) \(\mathstrut -\mathstrut 1603q^{81} \) \(\mathstrut -\mathstrut 1139q^{82} \) \(\mathstrut +\mathstrut 106q^{83} \) \(\mathstrut +\mathstrut 2454q^{84} \) \(\mathstrut +\mathstrut 592q^{85} \) \(\mathstrut +\mathstrut 742q^{86} \) \(\mathstrut +\mathstrut 998q^{87} \) \(\mathstrut +\mathstrut 412q^{88} \) \(\mathstrut +\mathstrut 1882q^{89} \) \(\mathstrut +\mathstrut 1760q^{90} \) \(\mathstrut +\mathstrut 748q^{91} \) \(\mathstrut -\mathstrut 552q^{92} \) \(\mathstrut -\mathstrut 1024q^{93} \) \(\mathstrut +\mathstrut 2281q^{94} \) \(\mathstrut -\mathstrut 536q^{95} \) \(\mathstrut +\mathstrut 1599q^{96} \) \(\mathstrut +\mathstrut 98q^{97} \) \(\mathstrut +\mathstrut 3036q^{98} \) \(\mathstrut -\mathstrut 1566q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(23))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 23
23.4.a.a \(1\) \(1.357\) \(\Q\) None \(-2\) \(-5\) \(-6\) \(-8\) \(-\) \(q-2q^{2}-5q^{3}-4q^{4}-6q^{5}+10q^{6}+\cdots\)
23.4.a.b \(4\) \(1.357\) 4.4.334189.1 None \(2\) \(7\) \(14\) \(16\) \(+\) \(q+(1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+(6+\cdots)q^{4}+\cdots\)