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Properties

Label 22.6.c
Level $22$
Weight $6$
Character orbit 22.c
Rep. character $\chi_{22}(3,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $20$
Newform subspaces $2$
Sturm bound $18$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 22.c (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 2 \)
Sturm bound: \(18\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(22, [\chi])\).

Total New Old
Modular forms 68 20 48
Cusp forms 52 20 32
Eisenstein series 16 0 16

Trace form

\( 20 q - 4 q^{2} + 20 q^{3} - 80 q^{4} + 14 q^{5} - 60 q^{6} - 278 q^{7} - 64 q^{8} + 215 q^{9} + O(q^{10}) \) \( 20 q - 4 q^{2} + 20 q^{3} - 80 q^{4} + 14 q^{5} - 60 q^{6} - 278 q^{7} - 64 q^{8} + 215 q^{9} + 1296 q^{10} + 1011 q^{11} + 480 q^{12} - 1992 q^{13} - 1496 q^{14} - 3466 q^{15} - 1280 q^{16} + 310 q^{17} + 928 q^{18} + 5711 q^{19} + 224 q^{20} + 6956 q^{21} + 484 q^{22} + 17372 q^{23} - 960 q^{24} - 23855 q^{25} - 8520 q^{26} - 32911 q^{27} + 1952 q^{28} - 9170 q^{29} + 14760 q^{30} + 22214 q^{31} + 4096 q^{32} + 65175 q^{33} + 21640 q^{34} - 31460 q^{35} - 15040 q^{36} + 8946 q^{37} - 32744 q^{38} - 23038 q^{39} - 15104 q^{40} - 30822 q^{41} + 1592 q^{42} + 31438 q^{43} + 7616 q^{44} + 72052 q^{45} - 38352 q^{46} - 59144 q^{47} + 5120 q^{48} - 68797 q^{49} + 12436 q^{50} - 12547 q^{51} + 26208 q^{52} + 104336 q^{53} + 122656 q^{54} + 31156 q^{55} + 11264 q^{56} - 47095 q^{57} + 16648 q^{58} - 109831 q^{59} + 16704 q^{60} + 41204 q^{61} - 80888 q^{62} + 57152 q^{63} - 20480 q^{64} - 166744 q^{65} - 268736 q^{66} - 10530 q^{67} + 4960 q^{68} + 116254 q^{69} + 114992 q^{70} - 27944 q^{71} - 22592 q^{72} + 189342 q^{73} - 36712 q^{74} + 121275 q^{75} + 113376 q^{76} - 170508 q^{77} + 206432 q^{78} + 182410 q^{79} + 31744 q^{80} + 337086 q^{81} + 251940 q^{82} + 21417 q^{83} - 207744 q^{84} - 423570 q^{85} - 400732 q^{86} - 746388 q^{87} - 87616 q^{88} - 436842 q^{89} - 84112 q^{90} + 42348 q^{91} - 10528 q^{92} + 97766 q^{93} + 184096 q^{94} + 845310 q^{95} - 20480 q^{96} + 112817 q^{97} + 378960 q^{98} + 179903 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(22, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
22.6.c.a 22.c 11.c $8$ $3.528$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(8\) \(20\) \(-30\) \(48\) $\mathrm{SU}(2)[C_{5}]$ \(q-4\beta _{3}q^{2}+(3+3\beta _{3}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
22.6.c.b 22.c 11.c $12$ $3.528$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-12\) \(0\) \(44\) \(-326\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-4+4\beta _{1}+4\beta _{2}-4\beta _{3})q^{2}+(2\beta _{1}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(22, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(22, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)