Properties

Label 11.6.c
Level 11
Weight 6
Character orbit c
Rep. character \(\chi_{11}(3,\cdot)\)
Character field \(\Q(\zeta_{5})\)
Dimension 16
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 6 \)
Character orbit: \([\chi]\) = 11.c (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newforms: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(11, [\chi])\).

Total New Old
Modular forms 24 24 0
Cusp forms 16 16 0
Eisenstein series 8 8 0

Trace form

\( 16q - q^{2} - 24q^{3} - 73q^{4} - 10q^{5} + 121q^{6} + 196q^{7} + 527q^{8} - 530q^{9} + O(q^{10}) \) \( 16q - q^{2} - 24q^{3} - 73q^{4} - 10q^{5} + 121q^{6} + 196q^{7} + 527q^{8} - 530q^{9} - 672q^{10} - 692q^{11} - 1562q^{12} + 1162q^{13} + 560q^{14} + 1796q^{15} + 6399q^{16} - 22q^{17} + 834q^{18} - 3236q^{19} - 5514q^{20} - 7772q^{21} - 13059q^{22} - 10848q^{23} + 13233q^{24} + 15686q^{25} + 16216q^{26} + 22500q^{27} + 8838q^{28} + 13070q^{29} - 22830q^{30} - 14764q^{31} - 58812q^{32} - 48544q^{33} - 26966q^{34} + 43368q^{35} + 63696q^{36} + 4638q^{37} + 68144q^{38} + 20300q^{39} + 52284q^{40} - 14806q^{41} - 69922q^{42} - 24376q^{43} - 104960q^{44} - 97480q^{45} + 50452q^{46} + 40364q^{47} + 30236q^{48} + 32246q^{49} + 10839q^{50} + 75564q^{51} - 80654q^{52} - 11654q^{53} + 43796q^{54} + 7052q^{55} + 70632q^{56} - 40020q^{57} + 10276q^{58} + 70804q^{59} + 46116q^{60} - 31446q^{61} - 153388q^{62} - 7064q^{63} + 17695q^{64} - 41284q^{65} + 48006q^{66} - 64200q^{67} - 94114q^{68} - 62412q^{69} - 103768q^{70} - 184380q^{71} - 14729q^{72} - 1750q^{73} + 306048q^{74} + 246596q^{75} + 174806q^{76} + 384646q^{77} + 360916q^{78} + 24324q^{79} - 386444q^{80} - 259412q^{81} - 316255q^{82} - 46028q^{83} - 271956q^{84} + 63914q^{85} + 22931q^{86} - 47592q^{87} + 211871q^{88} + 148364q^{89} - 347186q^{90} - 258448q^{91} - 58658q^{92} - 387478q^{93} - 55370q^{94} - 4716q^{95} + 328396q^{96} + 484296q^{97} + 743692q^{98} + 724964q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(11, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
11.6.c.a \(16\) \(1.764\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-1\) \(-24\) \(-10\) \(196\) \(q+(1-\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{7})q^{2}+\cdots\)