Properties

Label 11.5.d
Level 11
Weight 5
Character orbit d
Rep. character \(\chi_{11}(2,\cdot)\)
Character field \(\Q(\zeta_{10})\)
Dimension 12
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 11 \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 11.d (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 11 \)
Character field: \(\Q(\zeta_{10})\)
Newforms: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(11, [\chi])\).

Total New Old
Modular forms 20 20 0
Cusp forms 12 12 0
Eisenstein series 8 8 0

Trace form

\(12q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 7q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut +\mathstrut 75q^{6} \) \(\mathstrut -\mathstrut 80q^{7} \) \(\mathstrut -\mathstrut 245q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut +\mathstrut 7q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut +\mathstrut 75q^{6} \) \(\mathstrut -\mathstrut 80q^{7} \) \(\mathstrut -\mathstrut 245q^{8} \) \(\mathstrut +\mathstrut q^{9} \) \(\mathstrut -\mathstrut 43q^{11} \) \(\mathstrut +\mathstrut 594q^{12} \) \(\mathstrut +\mathstrut 250q^{13} \) \(\mathstrut +\mathstrut 610q^{14} \) \(\mathstrut +\mathstrut 1134q^{15} \) \(\mathstrut -\mathstrut 633q^{16} \) \(\mathstrut -\mathstrut 1250q^{17} \) \(\mathstrut -\mathstrut 3150q^{18} \) \(\mathstrut -\mathstrut 1025q^{19} \) \(\mathstrut +\mathstrut 752q^{20} \) \(\mathstrut -\mathstrut 35q^{22} \) \(\mathstrut +\mathstrut 1684q^{23} \) \(\mathstrut +\mathstrut 5345q^{24} \) \(\mathstrut +\mathstrut 197q^{25} \) \(\mathstrut +\mathstrut 3490q^{26} \) \(\mathstrut -\mathstrut 687q^{27} \) \(\mathstrut -\mathstrut 3580q^{28} \) \(\mathstrut -\mathstrut 2690q^{29} \) \(\mathstrut -\mathstrut 6740q^{30} \) \(\mathstrut -\mathstrut 1136q^{31} \) \(\mathstrut +\mathstrut 5939q^{33} \) \(\mathstrut +\mathstrut 2370q^{34} \) \(\mathstrut +\mathstrut 3610q^{35} \) \(\mathstrut -\mathstrut 514q^{36} \) \(\mathstrut -\mathstrut 336q^{37} \) \(\mathstrut +\mathstrut 1900q^{38} \) \(\mathstrut -\mathstrut 6880q^{39} \) \(\mathstrut -\mathstrut 2340q^{40} \) \(\mathstrut -\mathstrut 4550q^{41} \) \(\mathstrut +\mathstrut 1310q^{42} \) \(\mathstrut -\mathstrut 6268q^{44} \) \(\mathstrut +\mathstrut 5136q^{45} \) \(\mathstrut +\mathstrut 4150q^{46} \) \(\mathstrut +\mathstrut 24q^{47} \) \(\mathstrut +\mathstrut 344q^{48} \) \(\mathstrut +\mathstrut 827q^{49} \) \(\mathstrut +\mathstrut 8895q^{50} \) \(\mathstrut +\mathstrut 13155q^{51} \) \(\mathstrut +\mathstrut 14070q^{52} \) \(\mathstrut +\mathstrut 414q^{53} \) \(\mathstrut -\mathstrut 2738q^{55} \) \(\mathstrut -\mathstrut 21340q^{56} \) \(\mathstrut -\mathstrut 26925q^{57} \) \(\mathstrut +\mathstrut 2980q^{58} \) \(\mathstrut -\mathstrut 10011q^{59} \) \(\mathstrut -\mathstrut 6856q^{60} \) \(\mathstrut +\mathstrut 9460q^{61} \) \(\mathstrut -\mathstrut 6200q^{62} \) \(\mathstrut +\mathstrut 9150q^{63} \) \(\mathstrut -\mathstrut 2633q^{64} \) \(\mathstrut -\mathstrut 3210q^{66} \) \(\mathstrut +\mathstrut 12154q^{67} \) \(\mathstrut -\mathstrut 9400q^{68} \) \(\mathstrut -\mathstrut 9022q^{69} \) \(\mathstrut -\mathstrut 9380q^{70} \) \(\mathstrut +\mathstrut 17574q^{71} \) \(\mathstrut +\mathstrut 43045q^{72} \) \(\mathstrut +\mathstrut 27950q^{73} \) \(\mathstrut +\mathstrut 43270q^{74} \) \(\mathstrut -\mathstrut 1761q^{75} \) \(\mathstrut +\mathstrut 4090q^{77} \) \(\mathstrut -\mathstrut 42920q^{78} \) \(\mathstrut -\mathstrut 41540q^{79} \) \(\mathstrut -\mathstrut 2308q^{80} \) \(\mathstrut -\mathstrut 21080q^{81} \) \(\mathstrut -\mathstrut 28175q^{82} \) \(\mathstrut -\mathstrut 18665q^{83} \) \(\mathstrut +\mathstrut 26250q^{84} \) \(\mathstrut -\mathstrut 4230q^{85} \) \(\mathstrut -\mathstrut 10125q^{86} \) \(\mathstrut -\mathstrut 15125q^{88} \) \(\mathstrut +\mathstrut 5554q^{89} \) \(\mathstrut +\mathstrut 18400q^{90} \) \(\mathstrut +\mathstrut 7390q^{91} \) \(\mathstrut +\mathstrut 3904q^{92} \) \(\mathstrut +\mathstrut 36898q^{93} \) \(\mathstrut +\mathstrut 18920q^{94} \) \(\mathstrut +\mathstrut 14110q^{95} \) \(\mathstrut -\mathstrut 21140q^{96} \) \(\mathstrut +\mathstrut 20769q^{97} \) \(\mathstrut -\mathstrut 3269q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(11, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
11.5.d.a \(12\) \(1.137\) \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-5\) \(-6\) \(-18\) \(-80\) \(q+(-1-\beta _{2}-2\beta _{3}-\beta _{4}+\beta _{7})q^{2}+\cdots\)