Properties

Label 23.6.a
Level 23
Weight 6
Character orbit a
Rep. character \(\chi_{23}(1,\cdot)\)
Character field \(\Q\)
Dimension 9
Newforms 2
Sturm bound 12
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 23.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(23))\).

Total New Old
Modular forms 11 9 2
Cusp forms 9 9 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.
\(+\)\(3\)
\(-\)\(6\)

Trace form

\(9q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 128q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 137q^{6} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 883q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(9q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 128q^{4} \) \(\mathstrut -\mathstrut 16q^{5} \) \(\mathstrut +\mathstrut 137q^{6} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 883q^{9} \) \(\mathstrut -\mathstrut 166q^{10} \) \(\mathstrut +\mathstrut 78q^{11} \) \(\mathstrut -\mathstrut 287q^{12} \) \(\mathstrut -\mathstrut 324q^{13} \) \(\mathstrut -\mathstrut 968q^{14} \) \(\mathstrut -\mathstrut 410q^{15} \) \(\mathstrut -\mathstrut 1776q^{16} \) \(\mathstrut -\mathstrut 1296q^{17} \) \(\mathstrut +\mathstrut 1301q^{18} \) \(\mathstrut +\mathstrut 4392q^{19} \) \(\mathstrut -\mathstrut 5620q^{20} \) \(\mathstrut -\mathstrut 6518q^{21} \) \(\mathstrut -\mathstrut 620q^{22} \) \(\mathstrut +\mathstrut 1587q^{23} \) \(\mathstrut -\mathstrut 44q^{24} \) \(\mathstrut +\mathstrut 2619q^{25} \) \(\mathstrut +\mathstrut 6509q^{26} \) \(\mathstrut +\mathstrut 3896q^{27} \) \(\mathstrut -\mathstrut 694q^{28} \) \(\mathstrut +\mathstrut 10400q^{29} \) \(\mathstrut -\mathstrut 6274q^{30} \) \(\mathstrut +\mathstrut 10728q^{31} \) \(\mathstrut +\mathstrut 13256q^{32} \) \(\mathstrut +\mathstrut 11070q^{33} \) \(\mathstrut -\mathstrut 27438q^{34} \) \(\mathstrut -\mathstrut 3224q^{35} \) \(\mathstrut -\mathstrut 13101q^{36} \) \(\mathstrut +\mathstrut 34364q^{37} \) \(\mathstrut +\mathstrut 2700q^{38} \) \(\mathstrut +\mathstrut 10128q^{39} \) \(\mathstrut +\mathstrut 13670q^{40} \) \(\mathstrut -\mathstrut 27060q^{41} \) \(\mathstrut -\mathstrut 3712q^{42} \) \(\mathstrut -\mathstrut 34812q^{43} \) \(\mathstrut -\mathstrut 46034q^{44} \) \(\mathstrut -\mathstrut 35766q^{45} \) \(\mathstrut +\mathstrut 4232q^{46} \) \(\mathstrut -\mathstrut 584q^{47} \) \(\mathstrut -\mathstrut 12089q^{48} \) \(\mathstrut +\mathstrut 40309q^{49} \) \(\mathstrut -\mathstrut 52280q^{50} \) \(\mathstrut -\mathstrut 21294q^{51} \) \(\mathstrut -\mathstrut 10605q^{52} \) \(\mathstrut +\mathstrut 34630q^{53} \) \(\mathstrut +\mathstrut 35583q^{54} \) \(\mathstrut +\mathstrut 47140q^{55} \) \(\mathstrut +\mathstrut 87586q^{56} \) \(\mathstrut -\mathstrut 90320q^{57} \) \(\mathstrut +\mathstrut 85323q^{58} \) \(\mathstrut +\mathstrut 17784q^{59} \) \(\mathstrut +\mathstrut 78084q^{60} \) \(\mathstrut -\mathstrut 44262q^{61} \) \(\mathstrut -\mathstrut 23739q^{62} \) \(\mathstrut -\mathstrut 41588q^{63} \) \(\mathstrut +\mathstrut 39467q^{64} \) \(\mathstrut +\mathstrut 7954q^{65} \) \(\mathstrut -\mathstrut 27754q^{66} \) \(\mathstrut -\mathstrut 25822q^{67} \) \(\mathstrut +\mathstrut 8908q^{68} \) \(\mathstrut +\mathstrut 19044q^{69} \) \(\mathstrut +\mathstrut 257604q^{70} \) \(\mathstrut -\mathstrut 60156q^{71} \) \(\mathstrut -\mathstrut 174009q^{72} \) \(\mathstrut +\mathstrut 30456q^{73} \) \(\mathstrut -\mathstrut 125922q^{74} \) \(\mathstrut -\mathstrut 276344q^{75} \) \(\mathstrut +\mathstrut 189304q^{76} \) \(\mathstrut -\mathstrut 90064q^{77} \) \(\mathstrut +\mathstrut 272251q^{78} \) \(\mathstrut +\mathstrut 95068q^{79} \) \(\mathstrut -\mathstrut 176098q^{80} \) \(\mathstrut +\mathstrut 245081q^{81} \) \(\mathstrut +\mathstrut 211965q^{82} \) \(\mathstrut -\mathstrut 66458q^{83} \) \(\mathstrut -\mathstrut 402954q^{84} \) \(\mathstrut -\mathstrut 86596q^{85} \) \(\mathstrut +\mathstrut 90562q^{86} \) \(\mathstrut +\mathstrut 34592q^{87} \) \(\mathstrut -\mathstrut 277428q^{88} \) \(\mathstrut +\mathstrut 43642q^{89} \) \(\mathstrut -\mathstrut 258940q^{90} \) \(\mathstrut -\mathstrut 98618q^{91} \) \(\mathstrut +\mathstrut 50784q^{92} \) \(\mathstrut +\mathstrut 404918q^{93} \) \(\mathstrut -\mathstrut 134103q^{94} \) \(\mathstrut -\mathstrut 210740q^{95} \) \(\mathstrut -\mathstrut 268041q^{96} \) \(\mathstrut -\mathstrut 14240q^{97} \) \(\mathstrut -\mathstrut 727092q^{98} \) \(\mathstrut +\mathstrut 501192q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(23))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 23
23.6.a.a \(3\) \(3.689\) 3.3.7925.1 None \(-4\) \(-20\) \(-58\) \(-282\) \(+\) \(q+(-1+\beta _{1})q^{2}+(-7-2\beta _{1}-\beta _{2})q^{3}+\cdots\)
23.6.a.b \(6\) \(3.689\) \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(4\) \(16\) \(42\) \(300\) \(-\) \(q+(1-\beta _{1})q^{2}+(3-\beta _{1}+\beta _{4})q^{3}+(19+\cdots)q^{4}+\cdots\)