Properties

Label 23.12.a
Level 23
Weight 12
Character orbit a
Rep. character \(\chi_{23}(1,\cdot)\)
Character field \(\Q\)
Dimension 19
Newforms 2
Sturm bound 24
Trace bound 1

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Defining parameters

Level: \( N \) = \( 23 \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 23.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(23))\).

Total New Old
Modular forms 23 19 4
Cusp forms 21 19 2
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.
\(+\)\(11\)
\(-\)\(8\)

Trace form

\(19q \) \(\mathstrut -\mathstrut 1012q^{3} \) \(\mathstrut +\mathstrut 16384q^{4} \) \(\mathstrut -\mathstrut 10432q^{5} \) \(\mathstrut +\mathstrut 12233q^{6} \) \(\mathstrut +\mathstrut 105466q^{7} \) \(\mathstrut -\mathstrut 40071q^{8} \) \(\mathstrut +\mathstrut 1260757q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 1012q^{3} \) \(\mathstrut +\mathstrut 16384q^{4} \) \(\mathstrut -\mathstrut 10432q^{5} \) \(\mathstrut +\mathstrut 12233q^{6} \) \(\mathstrut +\mathstrut 105466q^{7} \) \(\mathstrut -\mathstrut 40071q^{8} \) \(\mathstrut +\mathstrut 1260757q^{9} \) \(\mathstrut -\mathstrut 109758q^{10} \) \(\mathstrut -\mathstrut 1062858q^{11} \) \(\mathstrut -\mathstrut 2604959q^{12} \) \(\mathstrut +\mathstrut 1222128q^{13} \) \(\mathstrut +\mathstrut 3646312q^{14} \) \(\mathstrut +\mathstrut 3346510q^{15} \) \(\mathstrut +\mathstrut 10241040q^{16} \) \(\mathstrut +\mathstrut 23260068q^{17} \) \(\mathstrut -\mathstrut 25179907q^{18} \) \(\mathstrut +\mathstrut 382840q^{19} \) \(\mathstrut +\mathstrut 6962684q^{20} \) \(\mathstrut +\mathstrut 25725202q^{21} \) \(\mathstrut +\mathstrut 17415740q^{22} \) \(\mathstrut -\mathstrut 19309029q^{23} \) \(\mathstrut +\mathstrut 32557348q^{24} \) \(\mathstrut +\mathstrut 197070865q^{25} \) \(\mathstrut +\mathstrut 209496629q^{26} \) \(\mathstrut -\mathstrut 38237608q^{27} \) \(\mathstrut +\mathstrut 106649178q^{28} \) \(\mathstrut -\mathstrut 95586388q^{29} \) \(\mathstrut -\mathstrut 136471906q^{30} \) \(\mathstrut -\mathstrut 163252512q^{31} \) \(\mathstrut +\mathstrut 837948392q^{32} \) \(\mathstrut -\mathstrut 327863610q^{33} \) \(\mathstrut +\mathstrut 297154370q^{34} \) \(\mathstrut +\mathstrut 248488936q^{35} \) \(\mathstrut -\mathstrut 343536333q^{36} \) \(\mathstrut +\mathstrut 750518188q^{37} \) \(\mathstrut -\mathstrut 216096540q^{38} \) \(\mathstrut +\mathstrut 1051627080q^{39} \) \(\mathstrut +\mathstrut 328205590q^{40} \) \(\mathstrut -\mathstrut 1375634160q^{41} \) \(\mathstrut -\mathstrut 6158862544q^{42} \) \(\mathstrut +\mathstrut 3147831684q^{43} \) \(\mathstrut +\mathstrut 402422302q^{44} \) \(\mathstrut -\mathstrut 4638106350q^{45} \) \(\mathstrut -\mathstrut 411925952q^{46} \) \(\mathstrut -\mathstrut 5174732048q^{47} \) \(\mathstrut +\mathstrut 370802383q^{48} \) \(\mathstrut +\mathstrut 7012992143q^{49} \) \(\mathstrut -\mathstrut 8653744088q^{50} \) \(\mathstrut +\mathstrut 5720596506q^{51} \) \(\mathstrut -\mathstrut 1774949925q^{52} \) \(\mathstrut +\mathstrut 155731150q^{53} \) \(\mathstrut -\mathstrut 3574988121q^{54} \) \(\mathstrut -\mathstrut 20671629116q^{55} \) \(\mathstrut +\mathstrut 8631305314q^{56} \) \(\mathstrut -\mathstrut 19440326480q^{57} \) \(\mathstrut -\mathstrut 7122394101q^{58} \) \(\mathstrut +\mathstrut 16044567480q^{59} \) \(\mathstrut +\mathstrut 39279750516q^{60} \) \(\mathstrut -\mathstrut 1442882470q^{61} \) \(\mathstrut +\mathstrut 11943220917q^{62} \) \(\mathstrut +\mathstrut 31167155116q^{63} \) \(\mathstrut -\mathstrut 1073827621q^{64} \) \(\mathstrut -\mathstrut 22294710950q^{65} \) \(\mathstrut +\mathstrut 46515470870q^{66} \) \(\mathstrut +\mathstrut 43682546986q^{67} \) \(\mathstrut +\mathstrut 3395689084q^{68} \) \(\mathstrut -\mathstrut 6256125396q^{69} \) \(\mathstrut -\mathstrut 47993932556q^{70} \) \(\mathstrut -\mathstrut 7070730468q^{71} \) \(\mathstrut +\mathstrut 3663094407q^{72} \) \(\mathstrut -\mathstrut 3227563732q^{73} \) \(\mathstrut -\mathstrut 31549322634q^{74} \) \(\mathstrut +\mathstrut 1033548616q^{75} \) \(\mathstrut +\mathstrut 23537658280q^{76} \) \(\mathstrut -\mathstrut 25369490848q^{77} \) \(\mathstrut -\mathstrut 137039230277q^{78} \) \(\mathstrut -\mathstrut 5835545108q^{79} \) \(\mathstrut +\mathstrut 6642036542q^{80} \) \(\mathstrut +\mathstrut 177934952675q^{81} \) \(\mathstrut +\mathstrut 43399719725q^{82} \) \(\mathstrut +\mathstrut 27899376526q^{83} \) \(\mathstrut -\mathstrut 52533515418q^{84} \) \(\mathstrut +\mathstrut 175633300012q^{85} \) \(\mathstrut +\mathstrut 43215093946q^{86} \) \(\mathstrut -\mathstrut 134870993896q^{87} \) \(\mathstrut -\mathstrut 229314364564q^{88} \) \(\mathstrut +\mathstrut 47963046142q^{89} \) \(\mathstrut +\mathstrut 30811067900q^{90} \) \(\mathstrut +\mathstrut 81080069838q^{91} \) \(\mathstrut -\mathstrut 39544891392q^{92} \) \(\mathstrut -\mathstrut 60331743946q^{93} \) \(\mathstrut -\mathstrut 92889902095q^{94} \) \(\mathstrut -\mathstrut 319826718836q^{95} \) \(\mathstrut +\mathstrut 111158628927q^{96} \) \(\mathstrut -\mathstrut 124763057260q^{97} \) \(\mathstrut -\mathstrut 298731563076q^{98} \) \(\mathstrut +\mathstrut 283285847736q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(23))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 23
23.12.a.a \(8\) \(17.672\) \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-32\) \(-992\) \(-11466\) \(-54118\) \(-\) \(q+(-4-\beta _{1})q^{2}+(-124-\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
23.12.a.b \(11\) \(17.672\) \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(32\) \(-20\) \(1034\) \(159584\) \(+\) \(q+(3-\beta _{1})q^{2}+(-2+\beta _{1}-\beta _{2})q^{3}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(23))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(23)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)