Properties

Label 121.2.g
Level $121$
Weight $2$
Character orbit 121.g
Rep. character $\chi_{121}(4,\cdot)$
Character field $\Q(\zeta_{55})$
Dimension $400$
Newform subspaces $1$
Sturm bound $22$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 121 = 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 121.g (of order \(55\) and degree \(40\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 121 \)
Character field: \(\Q(\zeta_{55})\)
Newform subspaces: \( 1 \)
Sturm bound: \(22\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(121, [\chi])\).

Total New Old
Modular forms 480 480 0
Cusp forms 400 400 0
Eisenstein series 80 80 0

Trace form

\( 400 q - 44 q^{2} - 32 q^{3} - 34 q^{4} - 43 q^{5} - 22 q^{6} - 44 q^{7} - 44 q^{8} - 110 q^{9} + O(q^{10}) \) \( 400 q - 44 q^{2} - 32 q^{3} - 34 q^{4} - 43 q^{5} - 22 q^{6} - 44 q^{7} - 44 q^{8} - 110 q^{9} - 22 q^{10} - 33 q^{11} + 6 q^{12} - 11 q^{13} - 18 q^{14} + 16 q^{15} - 30 q^{16} - 44 q^{17} + 11 q^{18} - 44 q^{19} - 36 q^{20} - 11 q^{21} - 34 q^{23} + 77 q^{24} - 31 q^{25} - 38 q^{26} + 40 q^{27} - 44 q^{28} - 44 q^{29} - 11 q^{30} - 17 q^{31} - 44 q^{32} - 11 q^{33} - 76 q^{34} - 44 q^{35} + 57 q^{36} - 4 q^{37} + 34 q^{38} - 11 q^{39} + 33 q^{40} - 44 q^{41} + 3 q^{42} - 44 q^{43} - 33 q^{44} - 12 q^{45} - 44 q^{46} - 36 q^{47} + 9 q^{48} + 16 q^{49} + 88 q^{50} + 154 q^{51} + 110 q^{52} + 78 q^{53} + 231 q^{54} + 44 q^{55} - 55 q^{56} + 66 q^{57} + 73 q^{58} - 33 q^{59} + 15 q^{60} - 44 q^{61} + 11 q^{62} + 121 q^{63} + 96 q^{64} - 11 q^{65} - 41 q^{67} - 44 q^{68} + 8 q^{69} + 24 q^{70} + 15 q^{71} + 77 q^{72} - 22 q^{73} - 44 q^{74} + 7 q^{75} + 176 q^{76} + 88 q^{77} - 21 q^{78} + 44 q^{79} + 171 q^{80} + 37 q^{81} + 22 q^{82} - 44 q^{83} - 11 q^{84} + 66 q^{85} - 20 q^{86} - 11 q^{87} + 77 q^{88} + 3 q^{89} + 264 q^{90} + 79 q^{91} + 228 q^{92} + 49 q^{93} + 143 q^{94} + 44 q^{95} + 121 q^{96} + 10 q^{97} + 132 q^{98} + 143 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(121, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
121.2.g.a 121.g 121.g $400$ $0.966$ None \(-44\) \(-32\) \(-43\) \(-44\) $\mathrm{SU}(2)[C_{55}]$