Properties

Label 11.4.c
Level $11$
Weight $4$
Character orbit 11.c
Rep. character $\chi_{11}(3,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $8$
Newform subspaces $1$
Sturm bound $4$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 11.c (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 1 \)
Sturm bound: \(4\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(11, [\chi])\).

Total New Old
Modular forms 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 0

Trace form

\( 8 q - 7 q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - 29 q^{6} - 35 q^{7} + 47 q^{8} + 31 q^{9} + O(q^{10}) \) \( 8 q - 7 q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - 29 q^{6} - 35 q^{7} + 47 q^{8} + 31 q^{9} + 40 q^{10} + 67 q^{11} + 190 q^{12} - 65 q^{13} - 196 q^{14} - 121 q^{15} - 377 q^{16} - 31 q^{17} - 102 q^{18} + 148 q^{19} + 342 q^{20} + 334 q^{21} + 647 q^{22} - 12 q^{23} - 447 q^{24} - 201 q^{25} - 140 q^{26} + 72 q^{27} - 42 q^{28} - 199 q^{29} - 114 q^{30} - 361 q^{31} + 324 q^{32} - 232 q^{33} - 298 q^{34} + 237 q^{35} + 120 q^{36} + 81 q^{37} - 52 q^{38} + 365 q^{39} + 532 q^{40} - 31 q^{41} + 170 q^{42} - 650 q^{43} - 1208 q^{44} + 452 q^{45} + 1204 q^{46} + 857 q^{47} + 644 q^{48} + 1375 q^{49} - 147 q^{50} - 246 q^{51} - 590 q^{52} - 1493 q^{53} - 3100 q^{54} - 1583 q^{55} - 1560 q^{56} + 102 q^{57} + 1392 q^{58} + 676 q^{59} + 1068 q^{60} - 525 q^{61} + 2456 q^{62} - 68 q^{63} + 471 q^{64} + 1790 q^{65} + 1014 q^{66} + 86 q^{67} + 710 q^{68} - 42 q^{69} - 144 q^{70} + 1143 q^{71} + 919 q^{72} - 2155 q^{73} - 1476 q^{74} - 160 q^{75} - 242 q^{76} - 2015 q^{77} - 1340 q^{78} - 861 q^{79} - 1916 q^{80} - 26 q^{81} - 3497 q^{82} + 52 q^{83} - 84 q^{84} + 2383 q^{85} + 1061 q^{86} + 2310 q^{87} + 4543 q^{88} + 3782 q^{89} - 1682 q^{90} + 135 q^{91} - 2450 q^{92} - 2077 q^{93} + 702 q^{94} - 1317 q^{95} + 1252 q^{96} - 1344 q^{97} + 2740 q^{98} + 2099 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(11, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
11.4.c.a \(8\) \(0.649\) 8.0.\(\cdots\).1 None \(-7\) \(-3\) \(-7\) \(-35\) \(q+(-1+\beta _{1}+\beta _{2}-\beta _{4})q^{2}+(-2-2\beta _{2}+\cdots)q^{3}+\cdots\)