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Properties

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

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Defining parameters

Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 22.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
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

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

Display 100 coefficients 10 coefficients

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

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

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