Properties

Label 23.12.a
Level $23$
Weight $12$
Character orbit 23.a
Rep. character $\chi_{23}(1,\cdot)$
Character field $\Q$
Dimension $19$
Newform subspaces $2$
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: \(\Q\)
Newform subspaces: \( 2 \)
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 and the Fricke involution.

\(23\)Dim
\(+\)\(11\)
\(-\)\(8\)

Trace form

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

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(23))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 23
23.12.a.a 23.a 1.a $8$ $17.672$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-32\) \(-992\) \(-11466\) \(-54118\) $-$ $\mathrm{SU}(2)$ \(q+(-4-\beta _{1})q^{2}+(-124-\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
23.12.a.b 23.a 1.a $11$ $17.672$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(32\) \(-20\) \(1034\) \(159584\) $+$ $\mathrm{SU}(2)$ \(q+(3-\beta _{1})q^{2}+(-2+\beta _{1}-\beta _{2})q^{3}+\cdots\)

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

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