Properties

Label 121.4.g
Level $121$
Weight $4$
Character orbit 121.g
Rep. character $\chi_{121}(4,\cdot)$
Character field $\Q(\zeta_{55})$
Dimension $1280$
Newform subspaces $1$
Sturm bound $44$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 121 = 11^{2} \)
Weight: \( k \) \(=\) \( 4 \)
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: \(44\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(121, [\chi])\).

Total New Old
Modular forms 1360 1360 0
Cusp forms 1280 1280 0
Eisenstein series 80 80 0

Trace form

\( 1280 q - 37 q^{2} - 32 q^{3} + 73 q^{4} - 33 q^{5} + 73 q^{6} - 9 q^{7} - 91 q^{8} - 2748 q^{9} + O(q^{10}) \) \( 1280 q - 37 q^{2} - 32 q^{3} + 73 q^{4} - 33 q^{5} + 73 q^{6} - 9 q^{7} - 91 q^{8} - 2748 q^{9} + 48 q^{10} + 43 q^{11} + 323 q^{12} - 287 q^{13} - 120 q^{14} + 632 q^{15} + 785 q^{16} - 13 q^{17} + 443 q^{18} - 192 q^{19} - 302 q^{20} - 81 q^{21} - 1483 q^{22} + 790 q^{23} - 1324 q^{24} + 835 q^{25} + 168 q^{26} + 583 q^{27} - 2 q^{28} + 155 q^{29} + 367 q^{30} - 351 q^{31} - 368 q^{32} + 485 q^{33} - 18 q^{34} - 281 q^{35} + 1823 q^{36} - 1097 q^{37} - 362 q^{38} - 112 q^{39} - 3205 q^{40} - 13 q^{41} - 111 q^{42} + 606 q^{43} + 2539 q^{44} + 1888 q^{45} - 1248 q^{46} - 499 q^{47} - 701 q^{48} - 2081 q^{49} + 3931 q^{50} - 1976 q^{51} + 2724 q^{52} + 1993 q^{53} - 2345 q^{54} - 1893 q^{55} - 167 q^{56} + 3462 q^{57} + 1949 q^{58} - 918 q^{59} - 843 q^{60} + 481 q^{61} + 745 q^{62} + 7284 q^{63} - 5887 q^{64} - 2362 q^{65} + 1329 q^{66} - 264 q^{67} - 754 q^{68} + 565 q^{69} + 5580 q^{70} - 27 q^{71} + 4966 q^{72} + 4223 q^{73} + 1432 q^{74} + 789 q^{75} + 6941 q^{76} - 3441 q^{77} - 7413 q^{78} + 5525 q^{79} + 2135 q^{80} - 18615 q^{81} + 3827 q^{82} - 96 q^{83} + 337 q^{84} - 6563 q^{85} - 963 q^{86} - 2057 q^{87} - 1771 q^{88} + 4114 q^{89} + 15586 q^{90} - 3505 q^{91} - 6694 q^{92} + 9192 q^{93} - 14111 q^{94} - 6295 q^{95} - 8919 q^{96} + 1042 q^{97} - 3048 q^{98} + 13103 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(121, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
121.4.g.a 121.g 121.g $1280$ $7.139$ None \(-37\) \(-32\) \(-33\) \(-9\) $\mathrm{SU}(2)[C_{55}]$