Properties

Label 22.10.a
Level 22
Weight 10
Character orbit a
Rep. character \(\chi_{22}(1,\cdot)\)
Character field \(\Q\)
Dimension 7
Newforms 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: \(\Q\)
Newforms: \( 5 \)
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

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

Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(22))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 11
22.10.a.a \(1\) \(11.331\) \(\Q\) None \(16\) \(-41\) \(-1039\) \(-3482\) \(-\) \(-\) \(q+2^{4}q^{2}-41q^{3}+2^{8}q^{4}-1039q^{5}+\cdots\)
22.10.a.b \(1\) \(11.331\) \(\Q\) None \(16\) \(137\) \(-595\) \(11354\) \(-\) \(+\) \(q+2^{4}q^{2}+137q^{3}+2^{8}q^{4}-595q^{5}+\cdots\)
22.10.a.c \(1\) \(11.331\) \(\Q\) None \(16\) \(201\) \(2349\) \(-8806\) \(-\) \(+\) \(q+2^{4}q^{2}+201q^{3}+2^{8}q^{4}+2349q^{5}+\cdots\)
22.10.a.d \(2\) \(11.331\) \(\Q(\sqrt{889}) \) None \(-32\) \(-21\) \(-521\) \(-7490\) \(+\) \(-\) \(q-2^{4}q^{2}+(-6-9\beta )q^{3}+2^{8}q^{4}+(-212+\cdots)q^{5}+\cdots\)
22.10.a.e \(2\) \(11.331\) \(\Q(\sqrt{463}) \) None \(-32\) \(34\) \(-1478\) \(8196\) \(+\) \(+\) \(q-2^{4}q^{2}+(17+\beta )q^{3}+2^{8}q^{4}+(-739+\cdots)q^{5}+\cdots\)

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

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