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Properties

Label 22.12.c
Level $22$
Weight $12$
Character orbit 22.c
Rep. character $\chi_{22}(3,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $44$
Newform subspaces $2$
Sturm bound $36$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 22 = 2 \cdot 11 \)
Weight: \( k \) \(=\) \( 12 \)
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: \(36\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(22, [\chi])\).

Total New Old
Modular forms 140 44 96
Cusp forms 124 44 80
Eisenstein series 16 0 16

Trace form

\( 44 q + 32 q^{2} + 20 q^{3} - 11264 q^{4} - 12082 q^{5} + 34464 q^{6} - 146606 q^{7} + 32768 q^{8} - 594595 q^{9} + O(q^{10}) \) \( 44 q + 32 q^{2} + 20 q^{3} - 11264 q^{4} - 12082 q^{5} + 34464 q^{6} - 146606 q^{7} + 32768 q^{8} - 594595 q^{9} - 636544 q^{10} - 8361 q^{11} + 2611200 q^{12} + 845764 q^{13} - 6008000 q^{14} + 8229374 q^{15} - 11534336 q^{16} - 3381530 q^{17} - 17351936 q^{18} + 39334763 q^{19} - 12371968 q^{20} - 88571044 q^{21} - 5153632 q^{22} - 175061764 q^{23} + 35291136 q^{24} + 108306819 q^{25} - 216379584 q^{26} - 413233027 q^{27} + 126969856 q^{28} + 652945006 q^{29} + 521596224 q^{30} - 628768354 q^{31} - 134217728 q^{32} - 1459579935 q^{33} - 224800832 q^{34} + 2778773548 q^{35} - 672071680 q^{36} - 566978838 q^{37} - 1927226432 q^{38} + 521468282 q^{39} - 46268416 q^{40} + 3003734754 q^{41} + 550078784 q^{42} + 1263409494 q^{43} + 426684416 q^{44} + 3989097484 q^{45} - 2492816000 q^{46} - 1336000688 q^{47} + 20971520 q^{48} + 5487408345 q^{49} + 6687884896 q^{50} + 8336202065 q^{51} + 586500096 q^{52} + 4878697628 q^{53} - 26339447552 q^{54} - 1634010484 q^{55} + 343408640 q^{56} - 16884425905 q^{57} + 14687248064 q^{58} + 15774364661 q^{59} + 5104889856 q^{60} - 13797293480 q^{61} - 12860390336 q^{62} - 66658697584 q^{63} - 11811160064 q^{64} + 937937984 q^{65} - 3187802624 q^{66} + 27813613910 q^{67} - 3462686720 q^{68} + 925018498 q^{69} + 22796833664 q^{70} + 81622545376 q^{71} + 33011040256 q^{72} + 29638158206 q^{73} + 7839282752 q^{74} - 209701626561 q^{75} - 17428932608 q^{76} - 51060749616 q^{77} - 100069444864 q^{78} + 210659165346 q^{79} + 13870563328 q^{80} - 33275090502 q^{81} + 1734254560 q^{82} + 148016772621 q^{83} + 97833345024 q^{84} + 94210833862 q^{85} - 128281080160 q^{86} - 390454486596 q^{87} - 20272283648 q^{88} - 384163051566 q^{89} + 393231601280 q^{90} + 421806506364 q^{91} + 99137583104 q^{92} + 311626748078 q^{93} + 12099888384 q^{94} + 608707036950 q^{95} + 3087007744 q^{96} - 499226846841 q^{97} - 52089252480 q^{98} - 1274275514437 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(22, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
22.12.c.a 22.c 11.c $20$ $16.904$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(-160\) \(56\) \(-362\) \(-167178\) $\mathrm{SU}(2)[C_{5}]$ \(q+2^{5}\beta _{2}q^{2}+(7+\beta _{1}+7\beta _{2}+9\beta _{4}+\cdots)q^{3}+\cdots\)
22.12.c.b 22.c 11.c $24$ $16.904$ None \(192\) \(-36\) \(-11720\) \(20572\) $\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{12}^{\mathrm{old}}(22, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(22, [\chi]) \cong \) \(S_{12}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)