Properties

Label 22.10.a
Level $22$
Weight $10$
Character orbit 22.a
Rep. character $\chi_{22}(1,\cdot)$
Character field $\Q$
Dimension $7$
Newform subspaces $5$
Sturm bound $30$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 22.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 5 \)
Sturm bound: \(30\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(22))\).

Total New Old
Modular forms 29 7 22
Cusp forms 25 7 18
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.
\(+\)\(+\)\(+\)\(2\)
\(+\)\(-\)\(-\)\(2\)
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(3\)
Minus space\(-\)\(4\)

Trace form

\( 7 q - 16 q^{2} + 310 q^{3} + 1792 q^{4} - 1284 q^{5} + 4544 q^{6} - 228 q^{7} - 4096 q^{8} + 19137 q^{9} + O(q^{10}) \) \( 7 q - 16 q^{2} + 310 q^{3} + 1792 q^{4} - 1284 q^{5} + 4544 q^{6} - 228 q^{7} - 4096 q^{8} + 19137 q^{9} + 43424 q^{10} - 14641 q^{11} + 79360 q^{12} - 321226 q^{13} - 26240 q^{14} + 208986 q^{15} + 458752 q^{16} + 671574 q^{17} - 248528 q^{18} + 748676 q^{19} - 328704 q^{20} + 814492 q^{21} - 234256 q^{22} - 4191078 q^{23} + 1163264 q^{24} + 4616135 q^{25} - 3668192 q^{26} + 315406 q^{27} - 58368 q^{28} - 2970882 q^{29} + 10519680 q^{30} - 5384302 q^{31} - 1048576 q^{32} - 6354194 q^{33} + 6211296 q^{34} - 7181340 q^{35} + 4899072 q^{36} - 14308120 q^{37} - 1470272 q^{38} - 28007856 q^{39} + 11116544 q^{40} + 99402 q^{41} - 15327744 q^{42} - 39453128 q^{43} - 3748096 q^{44} + 25302178 q^{45} + 32024192 q^{46} + 113412672 q^{47} + 20316160 q^{48} + 53322279 q^{49} - 38915056 q^{50} + 25138484 q^{51} - 82233856 q^{52} + 53941458 q^{53} - 39243904 q^{54} - 26880876 q^{55} - 6717440 q^{56} + 382083328 q^{57} + 67895840 q^{58} - 570813054 q^{59} + 53500416 q^{60} - 112867034 q^{61} + 127960576 q^{62} - 84351808 q^{63} + 117440512 q^{64} + 138845244 q^{65} - 75898944 q^{66} - 340578718 q^{67} + 171922944 q^{68} - 343857994 q^{69} - 647438592 q^{70} + 538105422 q^{71} - 63623168 q^{72} + 337081074 q^{73} - 307911776 q^{74} + 1255576660 q^{75} + 191661056 q^{76} - 317943956 q^{77} + 111066752 q^{78} + 1125978948 q^{79} - 84148224 q^{80} - 2035520673 q^{81} - 535307936 q^{82} - 824211648 q^{83} + 208509952 q^{84} + 187705680 q^{85} - 185018048 q^{86} + 39168664 q^{87} - 59969536 q^{88} - 1464345612 q^{89} + 1768428832 q^{90} + 1345629152 q^{91} - 1072915968 q^{92} - 1543653210 q^{93} - 1223113984 q^{94} + 3709619880 q^{95} + 297795584 q^{96} + 3188391928 q^{97} + 2267562096 q^{98} - 899294143 q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(22))\) 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
22.10.a.a 22.a 1.a $1$ $11.331$ \(\Q\) None \(16\) \(-41\) \(-1039\) \(-3482\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2^{4}q^{2}-41q^{3}+2^{8}q^{4}-1039q^{5}+\cdots\)
22.10.a.b 22.a 1.a $1$ $11.331$ \(\Q\) None \(16\) \(137\) \(-595\) \(11354\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{4}q^{2}+137q^{3}+2^{8}q^{4}-595q^{5}+\cdots\)
22.10.a.c 22.a 1.a $1$ $11.331$ \(\Q\) None \(16\) \(201\) \(2349\) \(-8806\) $-$ $+$ $\mathrm{SU}(2)$ \(q+2^{4}q^{2}+201q^{3}+2^{8}q^{4}+2349q^{5}+\cdots\)
22.10.a.d 22.a 1.a $2$ $11.331$ \(\Q(\sqrt{889}) \) None \(-32\) \(-21\) \(-521\) \(-7490\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2^{4}q^{2}+(-6-9\beta )q^{3}+2^{8}q^{4}+(-212+\cdots)q^{5}+\cdots\)
22.10.a.e 22.a 1.a $2$ $11.331$ \(\Q(\sqrt{463}) \) None \(-32\) \(34\) \(-1478\) \(8196\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2^{4}q^{2}+(17+\beta )q^{3}+2^{8}q^{4}+(-739+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(22))\) into lower level spaces

\( S_{10}^{\mathrm{old}}(\Gamma_0(22)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)