Properties

Label 22.8.a
Level 22
Weight 8
Character orbit a
Rep. character \(\chi_{22}(1,\cdot)\)
Character field \(\Q\)
Dimension 5
Newforms 4
Sturm bound 24
Trace bound 3

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 22 = 2 \cdot 11 \)
Weight: \( k \) = \( 8 \)
Character orbit: \([\chi]\) = 22.a (trivial)
Character field: \(\Q\)
Newforms: \( 4 \)
Sturm bound: \(24\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(22))\).

Total New Old
Modular forms 23 5 18
Cusp forms 19 5 14
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.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(2\)
Plus space\(+\)\(3\)
Minus space\(-\)\(2\)

Trace form

\(5q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 28q^{3} \) \(\mathstrut +\mathstrut 320q^{4} \) \(\mathstrut +\mathstrut 282q^{5} \) \(\mathstrut -\mathstrut 928q^{6} \) \(\mathstrut +\mathstrut 104q^{7} \) \(\mathstrut +\mathstrut 512q^{8} \) \(\mathstrut +\mathstrut 5853q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(5q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 28q^{3} \) \(\mathstrut +\mathstrut 320q^{4} \) \(\mathstrut +\mathstrut 282q^{5} \) \(\mathstrut -\mathstrut 928q^{6} \) \(\mathstrut +\mathstrut 104q^{7} \) \(\mathstrut +\mathstrut 512q^{8} \) \(\mathstrut +\mathstrut 5853q^{9} \) \(\mathstrut -\mathstrut 5776q^{10} \) \(\mathstrut +\mathstrut 1331q^{11} \) \(\mathstrut +\mathstrut 1792q^{12} \) \(\mathstrut -\mathstrut 7562q^{13} \) \(\mathstrut +\mathstrut 28864q^{14} \) \(\mathstrut +\mathstrut 11136q^{15} \) \(\mathstrut +\mathstrut 20480q^{16} \) \(\mathstrut -\mathstrut 62166q^{17} \) \(\mathstrut -\mathstrut 21464q^{18} \) \(\mathstrut +\mathstrut 75196q^{19} \) \(\mathstrut +\mathstrut 18048q^{20} \) \(\mathstrut -\mathstrut 172232q^{21} \) \(\mathstrut +\mathstrut 10648q^{22} \) \(\mathstrut -\mathstrut 9792q^{23} \) \(\mathstrut -\mathstrut 59392q^{24} \) \(\mathstrut +\mathstrut 109911q^{25} \) \(\mathstrut -\mathstrut 2000q^{26} \) \(\mathstrut +\mathstrut 355240q^{27} \) \(\mathstrut +\mathstrut 6656q^{28} \) \(\mathstrut -\mathstrut 238506q^{29} \) \(\mathstrut -\mathstrut 83904q^{30} \) \(\mathstrut -\mathstrut 681704q^{31} \) \(\mathstrut +\mathstrut 32768q^{32} \) \(\mathstrut -\mathstrut 149072q^{33} \) \(\mathstrut +\mathstrut 258960q^{34} \) \(\mathstrut -\mathstrut 93168q^{35} \) \(\mathstrut +\mathstrut 374592q^{36} \) \(\mathstrut +\mathstrut 361954q^{37} \) \(\mathstrut +\mathstrut 141280q^{38} \) \(\mathstrut +\mathstrut 2190312q^{39} \) \(\mathstrut -\mathstrut 369664q^{40} \) \(\mathstrut -\mathstrut 800838q^{41} \) \(\mathstrut -\mathstrut 639744q^{42} \) \(\mathstrut -\mathstrut 1373532q^{43} \) \(\mathstrut +\mathstrut 85184q^{44} \) \(\mathstrut +\mathstrut 2233006q^{45} \) \(\mathstrut -\mathstrut 239296q^{46} \) \(\mathstrut -\mathstrut 252096q^{47} \) \(\mathstrut +\mathstrut 114688q^{48} \) \(\mathstrut +\mathstrut 535869q^{49} \) \(\mathstrut +\mathstrut 1223864q^{50} \) \(\mathstrut -\mathstrut 2295304q^{51} \) \(\mathstrut -\mathstrut 483968q^{52} \) \(\mathstrut +\mathstrut 34278q^{53} \) \(\mathstrut -\mathstrut 4066624q^{54} \) \(\mathstrut +\mathstrut 1349634q^{55} \) \(\mathstrut +\mathstrut 1847296q^{56} \) \(\mathstrut -\mathstrut 5983760q^{57} \) \(\mathstrut -\mathstrut 2608720q^{58} \) \(\mathstrut +\mathstrut 2526420q^{59} \) \(\mathstrut +\mathstrut 712704q^{60} \) \(\mathstrut +\mathstrut 6110982q^{61} \) \(\mathstrut +\mathstrut 1374976q^{62} \) \(\mathstrut +\mathstrut 2756408q^{63} \) \(\mathstrut +\mathstrut 1310720q^{64} \) \(\mathstrut -\mathstrut 5212764q^{65} \) \(\mathstrut +\mathstrut 1149984q^{66} \) \(\mathstrut +\mathstrut 1641004q^{67} \) \(\mathstrut -\mathstrut 3978624q^{68} \) \(\mathstrut -\mathstrut 1954036q^{69} \) \(\mathstrut +\mathstrut 6615936q^{70} \) \(\mathstrut +\mathstrut 2743728q^{71} \) \(\mathstrut -\mathstrut 1373696q^{72} \) \(\mathstrut -\mathstrut 8208982q^{73} \) \(\mathstrut +\mathstrut 3933808q^{74} \) \(\mathstrut -\mathstrut 10536284q^{75} \) \(\mathstrut +\mathstrut 4812544q^{76} \) \(\mathstrut +\mathstrut 1895344q^{77} \) \(\mathstrut -\mathstrut 2984128q^{78} \) \(\mathstrut -\mathstrut 8421376q^{79} \) \(\mathstrut +\mathstrut 1155072q^{80} \) \(\mathstrut +\mathstrut 16288077q^{81} \) \(\mathstrut +\mathstrut 4059856q^{82} \) \(\mathstrut +\mathstrut 2347068q^{83} \) \(\mathstrut -\mathstrut 11022848q^{84} \) \(\mathstrut +\mathstrut 8022948q^{85} \) \(\mathstrut -\mathstrut 8017376q^{86} \) \(\mathstrut +\mathstrut 23329960q^{87} \) \(\mathstrut +\mathstrut 681472q^{88} \) \(\mathstrut +\mathstrut 12976758q^{89} \) \(\mathstrut +\mathstrut 9087280q^{90} \) \(\mathstrut -\mathstrut 9888048q^{91} \) \(\mathstrut -\mathstrut 626688q^{92} \) \(\mathstrut -\mathstrut 28008564q^{93} \) \(\mathstrut -\mathstrut 3114112q^{94} \) \(\mathstrut +\mathstrut 485160q^{95} \) \(\mathstrut -\mathstrut 3801088q^{96} \) \(\mathstrut -\mathstrut 31697466q^{97} \) \(\mathstrut +\mathstrut 5325384q^{98} \) \(\mathstrut -\mathstrut 3784033q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(22))\) 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
22.8.a.a \(1\) \(6.872\) \(\Q\) None \(-8\) \(-19\) \(317\) \(-1030\) \(+\) \(-\) \(q-8q^{2}-19q^{3}+2^{6}q^{4}+317q^{5}+\cdots\)
22.8.a.b \(1\) \(6.872\) \(\Q\) None \(-8\) \(91\) \(185\) \(-722\) \(+\) \(+\) \(q-8q^{2}+91q^{3}+2^{6}q^{4}+185q^{5}+\cdots\)
22.8.a.c \(1\) \(6.872\) \(\Q\) None \(8\) \(-21\) \(-551\) \(62\) \(-\) \(+\) \(q+8q^{2}-21q^{3}+2^{6}q^{4}-551q^{5}+\cdots\)
22.8.a.d \(2\) \(6.872\) \(\Q(\sqrt{14881}) \) None \(16\) \(-23\) \(331\) \(1794\) \(-\) \(-\) \(q+8q^{2}+(-11-\beta )q^{3}+2^{6}q^{4}+(165+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(22))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_0(22)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)