↑

Properties

Label 22.12.a
Level $22$
Weight $12$
Character orbit 22.a
Rep. character $\chi_{22}(1,\cdot)$
Character field $\Q$
Dimension $11$
Newform subspaces $4$
Sturm bound $36$
Trace bound $3$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 22.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(36\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(22))\).

Total New Old
Modular forms 35 11 24
Cusp forms 31 11 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.

\(2\)\(11\)FrickeDim
\(+\)\(+\)$+$\(3\)
\(+\)\(-\)$-$\(3\)
\(-\)\(+\)$-$\(2\)
\(-\)\(-\)$+$\(3\)
Plus space\(+\)\(6\)
Minus space\(-\)\(5\)

Trace form

\( 11 q - 32 q^{2} - 20 q^{3} + 11264 q^{4} + 12082 q^{5} - 2944 q^{6} - 45224 q^{7} - 32768 q^{8} + 915375 q^{9} + O(q^{10}) \) \( 11 q - 32 q^{2} - 20 q^{3} + 11264 q^{4} + 12082 q^{5} - 2944 q^{6} - 45224 q^{7} - 32768 q^{8} + 915375 q^{9} - 363456 q^{10} + 161051 q^{11} - 20480 q^{12} - 875894 q^{13} - 335360 q^{14} + 472536 q^{15} + 11534336 q^{16} - 13102170 q^{17} + 1427296 q^{18} - 7740548 q^{19} + 12371968 q^{20} + 6889024 q^{21} + 5153632 q^{22} + 93614464 q^{23} - 3014656 q^{24} + 102028181 q^{25} - 20038336 q^{26} - 175002488 q^{27} - 46309376 q^{28} + 286587034 q^{29} - 199855104 q^{30} - 309055976 q^{31} - 33554432 q^{32} + 99851620 q^{33} + 519375552 q^{34} + 16432992 q^{35} + 937344000 q^{36} + 648119698 q^{37} - 167456128 q^{38} - 1959228072 q^{39} - 372178944 q^{40} + 391758926 q^{41} + 295677696 q^{42} - 2183911004 q^{43} + 164916224 q^{44} + 749597026 q^{45} - 1551425280 q^{46} - 3684676472 q^{47} - 20971520 q^{48} + 3700166595 q^{49} - 172337376 q^{50} + 380497640 q^{51} - 896915456 q^{52} - 9108206598 q^{53} + 7972846592 q^{54} - 4378332486 q^{55} - 343408640 q^{56} - 3849141920 q^{57} + 11874670656 q^{58} + 12074756484 q^{59} + 483876864 q^{60} + 16775683690 q^{61} - 23914092544 q^{62} + 24940101224 q^{63} + 11811160064 q^{64} - 9892919524 q^{65} + 5009330304 q^{66} - 19655325860 q^{67} - 13416622080 q^{68} - 21210197368 q^{69} + 3837970176 q^{70} + 43068243344 q^{71} + 1461551104 q^{72} - 19855221026 q^{73} - 20581162432 q^{74} - 33234655484 q^{75} - 7926321152 q^{76} + 16268727816 q^{77} + 63217593344 q^{78} - 98359292336 q^{79} + 12668895232 q^{80} + 127815100707 q^{81} - 30084194880 q^{82} + 97303283084 q^{83} + 7054360576 q^{84} - 71855645292 q^{85} - 63811647360 q^{86} - 99384630104 q^{87} + 5277319168 q^{88} + 218796781046 q^{89} - 83004021440 q^{90} - 41718652624 q^{91} + 95861211136 q^{92} - 76691269368 q^{93} + 62528030976 q^{94} - 133726589800 q^{95} - 3087007744 q^{96} - 197647267154 q^{97} - 354675106080 q^{98} + 141202591607 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(22))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 11
22.12.a.a 22.a 1.a $2$ $16.904$ \(\Q(\sqrt{331}) \) None \(64\) \(-426\) \(2290\) \(-86324\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{5}q^{2}+(-213+3\beta )q^{3}+2^{10}q^{4}+\cdots\)
22.12.a.b 22.a 1.a $3$ $16.904$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-96\) \(-70\) \(-5624\) \(-30576\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{5}q^{2}+(-23+\beta _{2})q^{3}+2^{10}q^{4}+\cdots\)
22.12.a.c 22.a 1.a $3$ $16.904$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(-96\) \(106\) \(17344\) \(13204\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{5}q^{2}+(35+\beta _{1})q^{3}+2^{10}q^{4}+(5771+\cdots)q^{5}+\cdots\)
22.12.a.d 22.a 1.a $3$ $16.904$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(96\) \(370\) \(-1928\) \(58472\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{5}q^{2}+(123-\beta _{1})q^{3}+2^{10}q^{4}+\cdots\)

Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(22))\) into lower level spaces

\( S_{12}^{\mathrm{old}}(\Gamma_0(22)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)