Properties

Label 23.14.a
Level $23$
Weight $14$
Character orbit 23.a
Rep. character $\chi_{23}(1,\cdot)$
Character field $\Q$
Dimension $25$
Newform subspaces $2$
Sturm bound $28$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 23 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 23.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(28\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(23))\).

Total New Old
Modular forms 27 25 2
Cusp forms 25 25 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 and the Fricke involution.

\(23\)Dim
\(+\)\(11\)
\(-\)\(14\)

Trace form

\( 25 q + 1196 q^{3} + 114688 q^{4} + 41864 q^{5} + 125657 q^{6} - 240342 q^{7} - 563007 q^{8} + 13202047 q^{9} + O(q^{10}) \) \( 25 q + 1196 q^{3} + 114688 q^{4} + 41864 q^{5} + 125657 q^{6} - 240342 q^{7} - 563007 q^{8} + 13202047 q^{9} - 6953886 q^{10} + 3424254 q^{11} + 22791073 q^{12} - 3490664 q^{13} - 50205176 q^{14} - 28644050 q^{15} + 474023696 q^{16} - 135727596 q^{17} - 205621099 q^{18} - 341445048 q^{19} + 606240620 q^{20} - 345889274 q^{21} + 940566460 q^{22} + 444107667 q^{23} + 2080167412 q^{24} + 5707730059 q^{25} - 5385254803 q^{26} - 4436931304 q^{27} + 5853083146 q^{28} + 3810786476 q^{29} + 11442567806 q^{30} + 1799585632 q^{31} - 6619174744 q^{32} + 5133616890 q^{33} - 13170897758 q^{34} + 23782469416 q^{35} + 75183334035 q^{36} + 11525568684 q^{37} + 75781295940 q^{38} - 43127180568 q^{39} - 128743572250 q^{40} + 145002072168 q^{41} - 25277013952 q^{42} - 58604447612 q^{43} - 53069251058 q^{44} + 157492593054 q^{45} + 18948593792 q^{46} + 35429743216 q^{47} + 351741460231 q^{48} + 213974265997 q^{49} - 65145427880 q^{50} - 676355759310 q^{51} - 229732522445 q^{52} - 439967840030 q^{53} + 601280684031 q^{54} - 1414782940 q^{55} - 797443080926 q^{56} + 9352876240 q^{57} - 963157700517 q^{58} + 383987395368 q^{59} - 973894635516 q^{60} - 448933336618 q^{61} - 2285847781179 q^{62} - 1552095304148 q^{63} + 3384285815403 q^{64} + 1235812490614 q^{65} - 1042470550762 q^{66} - 54327098862 q^{67} - 1343285730932 q^{68} + 431672652324 q^{69} + 1929267077444 q^{70} + 906636578556 q^{71} - 3877789267929 q^{72} + 2471834387276 q^{73} + 3081951055110 q^{74} + 2023908332536 q^{75} + 532529113944 q^{76} - 6016796934784 q^{77} + 19949815938331 q^{78} - 5141201392020 q^{79} + 10817763149342 q^{80} + 3472115224793 q^{81} - 10330138050515 q^{82} - 7738352470298 q^{83} - 16612845540234 q^{84} - 5369146154476 q^{85} - 13230853150550 q^{86} + 14889510925592 q^{87} + 38919144103372 q^{88} + 982554351274 q^{89} - 26903439734740 q^{90} + 5506348780934 q^{91} + 3638130008064 q^{92} + 17009166428738 q^{93} - 16070620293047 q^{94} + 13627974848620 q^{95} + 21692164998231 q^{96} - 10861928378620 q^{97} + 19471631897868 q^{98} - 20532495314808 q^{99} + O(q^{100}) \)

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(23))\) 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
23.14.a.a 23.a 1.a $11$ $24.663$ \(\mathbb{Q}[x]/(x^{11} - \cdots)\) None \(-64\) \(-860\) \(-10318\) \(-430944\) $+$ $\mathrm{SU}(2)$ \(q+(-6+\beta _{1})q^{2}+(-78-\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)
23.14.a.b 23.a 1.a $14$ $24.663$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(64\) \(2056\) \(52182\) \(190602\) $-$ $\mathrm{SU}(2)$ \(q+(5-\beta _{1})q^{2}+(148-2\beta _{1}+\beta _{2})q^{3}+\cdots\)