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Properties

Label 22.8.c
Level $22$
Weight $8$
Character orbit 22.c
Rep. character $\chi_{22}(3,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $28$
Newform subspaces $2$
Sturm bound $24$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
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: \(24\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(22, [\chi])\).

Total New Old
Modular forms 92 28 64
Cusp forms 76 28 48
Eisenstein series 16 0 16

Trace form

\( 28 q + 8 q^{2} - 52 q^{3} - 448 q^{4} + 138 q^{5} - 600 q^{6} - 166 q^{7} + 512 q^{8} - 7507 q^{9} + O(q^{10}) \) \( 28 q + 8 q^{2} - 52 q^{3} - 448 q^{4} + 138 q^{5} - 600 q^{6} - 166 q^{7} + 512 q^{8} - 7507 q^{9} - 7584 q^{10} - 9013 q^{11} + 4992 q^{12} + 28728 q^{13} + 9872 q^{14} - 76786 q^{15} - 28672 q^{16} + 20594 q^{17} + 49216 q^{18} + 9919 q^{19} + 8832 q^{20} - 37372 q^{21} - 1912 q^{22} + 78428 q^{23} - 38400 q^{24} + 539 q^{25} + 156432 q^{26} + 515945 q^{27} + 78976 q^{28} + 411706 q^{29} - 188496 q^{30} - 288890 q^{31} - 131072 q^{32} - 1505067 q^{33} - 307984 q^{34} + 740028 q^{35} + 65792 q^{36} + 410934 q^{37} + 943120 q^{38} - 286750 q^{39} + 88064 q^{40} - 1504346 q^{41} - 664624 q^{42} - 2695522 q^{43} - 1332992 q^{44} - 1476356 q^{45} + 2044128 q^{46} + 2799664 q^{47} - 212992 q^{48} + 5597785 q^{49} - 666344 q^{50} + 6431285 q^{51} - 1289088 q^{52} - 5633992 q^{53} - 3044096 q^{54} - 11779684 q^{55} - 806912 q^{56} + 13029515 q^{57} + 3275120 q^{58} + 4012745 q^{59} + 3998976 q^{60} + 10915804 q^{61} + 5896816 q^{62} - 9676672 q^{63} - 1835008 q^{64} - 16834136 q^{65} - 7617152 q^{66} - 19735266 q^{67} + 1318016 q^{68} + 20581138 q^{69} + 9454144 q^{70} + 20466128 q^{71} + 8704 q^{72} + 4690098 q^{73} - 6958512 q^{74} - 12617661 q^{75} - 4089984 q^{76} - 26386556 q^{77} - 10139008 q^{78} - 6031894 q^{79} + 606208 q^{80} + 18089226 q^{81} - 297864 q^{82} - 6822007 q^{83} + 4634112 q^{84} - 15165558 q^{85} + 6797448 q^{86} + 3063420 q^{87} - 1407488 q^{88} + 32409842 q^{89} - 648160 q^{90} + 28843284 q^{91} + 6832512 q^{92} - 8092294 q^{93} + 15950048 q^{94} - 30780610 q^{95} + 4587520 q^{96} - 10889261 q^{97} - 44339616 q^{98} - 18928921 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{8}^{\mathrm{new}}(22, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
22.8.c.a 22.c 11.c $12$ $6.872$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-24\) \(44\) \(220\) \(534\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-8+8\beta _{1}+8\beta _{2}+8\beta _{3})q^{2}+(5\beta _{1}+\cdots)q^{3}+\cdots\)
22.8.c.b 22.c 11.c $16$ $6.872$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(32\) \(-96\) \(-82\) \(-700\) $\mathrm{SU}(2)[C_{5}]$ \(q-8\beta _{2}q^{2}+(-10-10\beta _{2}+3\beta _{3}+3\beta _{5}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(22, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(22, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)