Properties

Label 22.4.a
Level $22$
Weight $4$
Character orbit 22.a
Rep. character $\chi_{22}(1,\cdot)$
Character field $\Q$
Dimension $3$
Newform subspaces $3$
Sturm bound $12$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 22.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(12\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(22))\).

Total New Old
Modular forms 11 3 8
Cusp forms 7 3 4
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.
\(+\)\(+\)\(+\)\(1\)
\(+\)\(-\)\(-\)\(1\)
\(-\)\(-\)\(+\)\(1\)
Plus space\(+\)\(2\)
Minus space\(-\)\(1\)

Trace form

\( 3 q - 2 q^{2} - 2 q^{3} + 12 q^{4} - 8 q^{5} + 8 q^{6} - 4 q^{7} - 8 q^{8} - 15 q^{9} + O(q^{10}) \) \( 3 q - 2 q^{2} - 2 q^{3} + 12 q^{4} - 8 q^{5} + 8 q^{6} - 4 q^{7} - 8 q^{8} - 15 q^{9} + 4 q^{10} + 11 q^{11} - 8 q^{12} - 138 q^{13} - 32 q^{14} + 186 q^{15} + 48 q^{16} + 126 q^{17} - 74 q^{18} - 12 q^{19} - 32 q^{20} - 140 q^{21} + 22 q^{22} - 14 q^{23} + 32 q^{24} + 191 q^{25} + 212 q^{26} - 170 q^{27} - 16 q^{28} + 142 q^{29} - 384 q^{30} - 6 q^{31} - 32 q^{32} - 110 q^{33} - 84 q^{34} - 348 q^{35} - 60 q^{36} - 228 q^{37} + 488 q^{38} + 288 q^{39} + 16 q^{40} + 122 q^{41} + 240 q^{42} + 88 q^{43} + 44 q^{44} - 494 q^{45} + 784 q^{46} + 568 q^{47} - 32 q^{48} - 669 q^{49} - 846 q^{50} + 884 q^{51} - 552 q^{52} + 786 q^{53} + 128 q^{54} - 396 q^{55} - 128 q^{56} - 176 q^{57} - 764 q^{58} - 870 q^{59} + 744 q^{60} - 458 q^{61} - 640 q^{62} + 656 q^{63} + 192 q^{64} + 716 q^{65} + 264 q^{66} + 330 q^{67} + 504 q^{68} + 554 q^{69} + 816 q^{70} - 1690 q^{71} - 296 q^{72} + 770 q^{73} - 1180 q^{74} - 1484 q^{75} - 48 q^{76} + 132 q^{77} - 640 q^{78} - 508 q^{79} - 128 q^{80} - 501 q^{81} + 1628 q^{82} + 1616 q^{83} - 560 q^{84} + 2568 q^{85} + 264 q^{86} - 392 q^{87} + 88 q^{88} + 824 q^{89} + 1300 q^{90} - 448 q^{91} - 56 q^{92} - 822 q^{93} - 560 q^{94} - 1480 q^{95} + 128 q^{96} - 236 q^{97} + 366 q^{98} + 77 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(22))\) 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
22.4.a.a 22.a 1.a $1$ $1.298$ \(\Q\) None \(-2\) \(-7\) \(-19\) \(14\) $+$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-7q^{3}+4q^{4}-19q^{5}+14q^{6}+\cdots\)
22.4.a.b 22.a 1.a $1$ $1.298$ \(\Q\) None \(-2\) \(4\) \(14\) \(-8\) $+$ $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{3}+4q^{4}+14q^{5}-8q^{6}+\cdots\)
22.4.a.c 22.a 1.a $1$ $1.298$ \(\Q\) None \(2\) \(1\) \(-3\) \(-10\) $-$ $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+q^{3}+4q^{4}-3q^{5}+2q^{6}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(22))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(22)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 2}\)