Properties

Label 22.6.a
Level $22$
Weight $6$
Character orbit 22.a
Rep. character $\chi_{22}(1,\cdot)$
Character field $\Q$
Dimension $5$
Newform subspaces $4$
Sturm bound $18$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 22.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(18\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(22))\).

Total New Old
Modular forms 17 5 12
Cusp forms 13 5 8
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.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(+\)\(-\)\(2\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(3\)

Trace form

\( 5 q + 4 q^{2} - 20 q^{3} + 80 q^{4} - 14 q^{5} + 80 q^{6} - 312 q^{7} + 64 q^{8} + 885 q^{9} + O(q^{10}) \) \( 5 q + 4 q^{2} - 20 q^{3} + 80 q^{4} - 14 q^{5} + 80 q^{6} - 312 q^{7} + 64 q^{8} + 885 q^{9} - 296 q^{10} - 121 q^{11} - 320 q^{12} + 982 q^{13} - 704 q^{14} - 3024 q^{15} + 1280 q^{16} - 1110 q^{17} + 3892 q^{18} - 3476 q^{19} - 224 q^{20} + 1864 q^{21} - 484 q^{22} + 328 q^{23} + 1280 q^{24} + 4495 q^{25} - 8200 q^{26} - 584 q^{27} - 4992 q^{28} + 7030 q^{29} + 1920 q^{30} + 11776 q^{31} + 1024 q^{32} - 9680 q^{33} - 6360 q^{34} + 35520 q^{35} + 14160 q^{36} - 24566 q^{37} - 8176 q^{38} - 33192 q^{39} - 4736 q^{40} - 8758 q^{41} + 25248 q^{42} + 22292 q^{43} - 1936 q^{44} - 49802 q^{45} - 14048 q^{46} - 7736 q^{47} - 5120 q^{48} + 20397 q^{49} - 5316 q^{50} + 57992 q^{51} + 15712 q^{52} - 11826 q^{53} - 6016 q^{54} + 13794 q^{55} - 11264 q^{56} + 15520 q^{57} + 16792 q^{58} + 44436 q^{59} - 48384 q^{60} - 2314 q^{61} + 59648 q^{62} - 149272 q^{63} + 20480 q^{64} + 52004 q^{65} - 17424 q^{66} + 26380 q^{67} - 17760 q^{68} - 20884 q^{69} + 10848 q^{70} - 11656 q^{71} + 62272 q^{72} - 169782 q^{73} + 128792 q^{74} + 70180 q^{75} - 55616 q^{76} + 5808 q^{77} + 128 q^{78} - 92640 q^{79} - 3584 q^{80} + 333309 q^{81} - 129400 q^{82} + 91868 q^{83} + 29824 q^{84} - 92220 q^{85} - 167088 q^{86} - 190712 q^{87} - 7744 q^{88} - 24538 q^{89} - 426248 q^{90} - 31568 q^{91} + 5248 q^{92} + 444204 q^{93} + 269344 q^{94} - 125800 q^{95} + 20480 q^{96} - 155002 q^{97} + 53220 q^{98} + 85547 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(22))\) 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
22.6.a.a 22.a 1.a $1$ $3.528$ \(\Q\) None \(-4\) \(-21\) \(81\) \(98\) $+$ $-$ $\mathrm{SU}(2)$ \(q-4q^{2}-21q^{3}+2^{4}q^{4}+3^{4}q^{5}+84q^{6}+\cdots\)
22.6.a.b 22.a 1.a $1$ $3.528$ \(\Q\) None \(-4\) \(1\) \(-51\) \(-166\) $+$ $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+q^{3}+2^{4}q^{4}-51q^{5}-4q^{6}+\cdots\)
22.6.a.c 22.a 1.a $1$ $3.528$ \(\Q\) None \(4\) \(-29\) \(-31\) \(-230\) $-$ $-$ $\mathrm{SU}(2)$ \(q+4q^{2}-29q^{3}+2^{4}q^{4}-31q^{5}-116q^{6}+\cdots\)
22.6.a.d 22.a 1.a $2$ $3.528$ \(\Q(\sqrt{793}) \) None \(8\) \(29\) \(-13\) \(-14\) $-$ $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+(15-\beta )q^{3}+2^{4}q^{4}+(-9+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(22))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_0(22)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)