Properties

Label 14.5.d
Level 14
Weight 5
Character orbit d
Rep. character \(\chi_{14}(3,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 4
Newforms 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 14.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(14, [\chi])\).

Total New Old
Modular forms 20 4 16
Cusp forms 12 4 8
Eisenstein series 8 0 8

Trace form

\(4q \) \(\mathstrut -\mathstrut 18q^{3} \) \(\mathstrut -\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 54q^{5} \) \(\mathstrut -\mathstrut 28q^{7} \) \(\mathstrut +\mathstrut 84q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 18q^{3} \) \(\mathstrut -\mathstrut 16q^{4} \) \(\mathstrut +\mathstrut 54q^{5} \) \(\mathstrut -\mathstrut 28q^{7} \) \(\mathstrut +\mathstrut 84q^{9} \) \(\mathstrut -\mathstrut 96q^{10} \) \(\mathstrut -\mathstrut 54q^{11} \) \(\mathstrut +\mathstrut 144q^{12} \) \(\mathstrut -\mathstrut 708q^{15} \) \(\mathstrut -\mathstrut 128q^{16} \) \(\mathstrut +\mathstrut 918q^{17} \) \(\mathstrut +\mathstrut 576q^{18} \) \(\mathstrut +\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 378q^{21} \) \(\mathstrut +\mathstrut 192q^{22} \) \(\mathstrut -\mathstrut 486q^{23} \) \(\mathstrut -\mathstrut 768q^{24} \) \(\mathstrut -\mathstrut 572q^{25} \) \(\mathstrut -\mathstrut 1728q^{26} \) \(\mathstrut +\mathstrut 1456q^{28} \) \(\mathstrut +\mathstrut 3240q^{29} \) \(\mathstrut +\mathstrut 1152q^{30} \) \(\mathstrut -\mathstrut 546q^{31} \) \(\mathstrut +\mathstrut 1062q^{33} \) \(\mathstrut -\mathstrut 1890q^{35} \) \(\mathstrut -\mathstrut 1344q^{36} \) \(\mathstrut -\mathstrut 446q^{37} \) \(\mathstrut -\mathstrut 4320q^{38} \) \(\mathstrut -\mathstrut 3312q^{39} \) \(\mathstrut +\mathstrut 768q^{40} \) \(\mathstrut +\mathstrut 5376q^{42} \) \(\mathstrut +\mathstrut 2344q^{43} \) \(\mathstrut -\mathstrut 432q^{44} \) \(\mathstrut +\mathstrut 5724q^{45} \) \(\mathstrut +\mathstrut 3840q^{46} \) \(\mathstrut +\mathstrut 702q^{47} \) \(\mathstrut -\mathstrut 9212q^{49} \) \(\mathstrut -\mathstrut 3456q^{50} \) \(\mathstrut +\mathstrut 318q^{51} \) \(\mathstrut -\mathstrut 384q^{52} \) \(\mathstrut +\mathstrut 2754q^{53} \) \(\mathstrut -\mathstrut 1440q^{54} \) \(\mathstrut -\mathstrut 17460q^{57} \) \(\mathstrut +\mathstrut 384q^{58} \) \(\mathstrut +\mathstrut 12366q^{59} \) \(\mathstrut +\mathstrut 2832q^{60} \) \(\mathstrut +\mathstrut 7686q^{61} \) \(\mathstrut +\mathstrut 6468q^{63} \) \(\mathstrut +\mathstrut 2048q^{64} \) \(\mathstrut -\mathstrut 3024q^{65} \) \(\mathstrut -\mathstrut 3456q^{66} \) \(\mathstrut -\mathstrut 5062q^{67} \) \(\mathstrut -\mathstrut 7344q^{68} \) \(\mathstrut -\mathstrut 2016q^{70} \) \(\mathstrut +\mathstrut 18792q^{71} \) \(\mathstrut +\mathstrut 4608q^{72} \) \(\mathstrut -\mathstrut 17274q^{73} \) \(\mathstrut -\mathstrut 4320q^{74} \) \(\mathstrut -\mathstrut 5220q^{75} \) \(\mathstrut +\mathstrut 4914q^{77} \) \(\mathstrut +\mathstrut 8832q^{78} \) \(\mathstrut +\mathstrut 794q^{79} \) \(\mathstrut -\mathstrut 3456q^{80} \) \(\mathstrut -\mathstrut 4338q^{81} \) \(\mathstrut +\mathstrut 9984q^{82} \) \(\mathstrut -\mathstrut 5040q^{84} \) \(\mathstrut +\mathstrut 10380q^{85} \) \(\mathstrut -\mathstrut 10368q^{86} \) \(\mathstrut -\mathstrut 12276q^{87} \) \(\mathstrut -\mathstrut 768q^{88} \) \(\mathstrut -\mathstrut 12474q^{89} \) \(\mathstrut +\mathstrut 2688q^{91} \) \(\mathstrut +\mathstrut 7776q^{92} \) \(\mathstrut +\mathstrut 18918q^{93} \) \(\mathstrut +\mathstrut 15168q^{94} \) \(\mathstrut +\mathstrut 8910q^{95} \) \(\mathstrut +\mathstrut 6144q^{96} \) \(\mathstrut -\mathstrut 11448q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(14, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
14.5.d.a \(4\) \(1.447\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(-18\) \(54\) \(-28\) \(q+\beta _{1}q^{2}+(-6+2\beta _{1}-3\beta _{2}-2\beta _{3})q^{3}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(14, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)