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Properties

Label 21.14.a
Level $21$
Weight $14$
Character orbit 21.a
Rep. character $\chi_{21}(1,\cdot)$
Character field $\Q$
Dimension $12$
Newform subspaces $4$
Sturm bound $37$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 21 = 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 21.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(37\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(21))\).

Total New Old
Modular forms 36 12 24
Cusp forms 32 12 20
Eisenstein series 4 0 4

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(7\)FrickeDim
\(+\)\(+\)$+$\(3\)
\(+\)\(-\)$-$\(3\)
\(-\)\(+\)$-$\(4\)
\(-\)\(-\)$+$\(2\)
Plus space\(+\)\(5\)
Minus space\(-\)\(7\)

Trace form

\( 12 q + 130 q^{2} + 57346 q^{4} - 83728 q^{5} + 154548 q^{6} - 235298 q^{7} + 1540110 q^{8} + 6377292 q^{9} + O(q^{10}) \) \( 12 q + 130 q^{2} + 57346 q^{4} - 83728 q^{5} + 154548 q^{6} - 235298 q^{7} + 1540110 q^{8} + 6377292 q^{9} + 5422508 q^{10} + 7492472 q^{11} - 23730408 q^{12} - 65055448 q^{13} + 42588938 q^{14} - 67400424 q^{15} + 334776466 q^{16} + 427552512 q^{17} + 69087330 q^{18} - 373078672 q^{19} - 898859300 q^{20} - 171532242 q^{21} + 1449073376 q^{22} - 208026264 q^{23} + 2893602204 q^{24} + 4483865092 q^{25} - 7011075020 q^{26} - 643069434 q^{28} + 11886235448 q^{29} - 14232710232 q^{30} - 193381664 q^{31} + 25254804470 q^{32} - 261186120 q^{33} + 30811847580 q^{34} + 3346408156 q^{35} + 30476015586 q^{36} - 41354635592 q^{37} - 41511460112 q^{38} - 59393122992 q^{39} + 227357920356 q^{40} - 28455092240 q^{41} - 10978063488 q^{42} + 74436737280 q^{43} - 177091782176 q^{44} - 44496492048 q^{45} - 23697680952 q^{46} + 168469210416 q^{47} - 3179431440 q^{48} + 166095446412 q^{49} - 557731687138 q^{50} - 364807258920 q^{51} - 109283464092 q^{52} + 181972053480 q^{53} + 82133143668 q^{54} + 276381701008 q^{55} - 139138060446 q^{56} - 80529620688 q^{57} - 1411619861860 q^{58} - 770582212944 q^{59} - 156113040528 q^{60} + 1347847387448 q^{61} - 1512209585856 q^{62} - 125047004418 q^{63} + 3794250505098 q^{64} - 3655028353312 q^{65} + 1267579292184 q^{66} - 1423643980720 q^{67} + 9649348962492 q^{68} + 630353568744 q^{69} - 2502611174756 q^{70} + 3238709590296 q^{71} + 818477598510 q^{72} - 1139252667704 q^{73} - 9430390532868 q^{74} + 3202403711328 q^{75} - 3602877036576 q^{76} - 3399877273520 q^{77} + 568101581856 q^{78} - 3187408488960 q^{79} - 3638456079332 q^{80} + 3389154437772 q^{81} + 14629438291612 q^{82} + 11063385068928 q^{83} - 2107788189696 q^{84} - 6850896099072 q^{85} + 8116793312312 q^{86} + 5578216554240 q^{87} + 5571626821392 q^{88} - 3296900727472 q^{89} + 2881743074028 q^{90} - 3603206275452 q^{91} - 8497983608184 q^{92} + 1252554188112 q^{93} - 57513928389792 q^{94} - 6168842755360 q^{95} + 14014238790996 q^{96} + 48056821743208 q^{97} + 1799367336130 q^{98} + 3981806812152 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(21))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 7
21.14.a.a 21.a 1.a $2$ $22.518$ \(\Q(\sqrt{3}) \) None \(144\) \(1458\) \(-52560\) \(235298\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(72+\beta )q^{2}+3^{6}q^{3}+(-656+12^{2}\beta )q^{4}+\cdots\)
21.14.a.b 21.a 1.a $3$ $22.518$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-143\) \(-2187\) \(-20554\) \(-352947\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(-48+\beta _{1})q^{2}-3^{6}q^{3}+(5921-65\beta _{1}+\cdots)q^{4}+\cdots\)
21.14.a.c 21.a 1.a $3$ $22.518$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(102\) \(-2187\) \(24918\) \(352947\) $+$ $-$ $\mathrm{SU}(2)$ \(q+(34-\beta _{1})q^{2}-3^{6}q^{3}+(9084-18\beta _{1}+\cdots)q^{4}+\cdots\)
21.14.a.d 21.a 1.a $4$ $22.518$ \(\mathbb{Q}[x]/(x^{4} - \cdots)\) None \(27\) \(2916\) \(-35532\) \(-470596\) $-$ $+$ $\mathrm{SU}(2)$ \(q+(7-\beta _{1})q^{2}+3^{6}q^{3}+(3446-75\beta _{1}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(21))\) into lower level spaces

\( S_{14}^{\mathrm{old}}(\Gamma_0(21)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)