Properties

Label 5.5.c
Level 5
Weight 5
Character orbit c
Rep. character \(\chi_{5}(2,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 2
Newforms 1
Sturm bound 2
Trace bound 0

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Defining parameters

Level: \( N \) = \( 5 \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 5.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

Trace form

\(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 40q^{5} \) \(\mathstrut +\mathstrut 24q^{6} \) \(\mathstrut -\mathstrut 52q^{7} \) \(\mathstrut -\mathstrut 60q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 40q^{5} \) \(\mathstrut +\mathstrut 24q^{6} \) \(\mathstrut -\mathstrut 52q^{7} \) \(\mathstrut -\mathstrut 60q^{8} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut -\mathstrut 16q^{11} \) \(\mathstrut +\mathstrut 168q^{12} \) \(\mathstrut +\mathstrut 278q^{13} \) \(\mathstrut -\mathstrut 420q^{15} \) \(\mathstrut -\mathstrut 328q^{16} \) \(\mathstrut -\mathstrut 2q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 420q^{20} \) \(\mathstrut +\mathstrut 624q^{21} \) \(\mathstrut +\mathstrut 16q^{22} \) \(\mathstrut -\mathstrut 332q^{23} \) \(\mathstrut +\mathstrut 350q^{25} \) \(\mathstrut -\mathstrut 556q^{26} \) \(\mathstrut -\mathstrut 1080q^{27} \) \(\mathstrut -\mathstrut 728q^{28} \) \(\mathstrut +\mathstrut 480q^{30} \) \(\mathstrut +\mathstrut 1144q^{31} \) \(\mathstrut +\mathstrut 1288q^{32} \) \(\mathstrut +\mathstrut 96q^{33} \) \(\mathstrut -\mathstrut 260q^{35} \) \(\mathstrut +\mathstrut 252q^{36} \) \(\mathstrut -\mathstrut 502q^{37} \) \(\mathstrut +\mathstrut 360q^{38} \) \(\mathstrut -\mathstrut 2100q^{40} \) \(\mathstrut -\mathstrut 3376q^{41} \) \(\mathstrut -\mathstrut 624q^{42} \) \(\mathstrut +\mathstrut 2948q^{43} \) \(\mathstrut -\mathstrut 270q^{45} \) \(\mathstrut +\mathstrut 664q^{46} \) \(\mathstrut +\mathstrut 4948q^{47} \) \(\mathstrut +\mathstrut 1968q^{48} \) \(\mathstrut +\mathstrut 850q^{50} \) \(\mathstrut +\mathstrut 24q^{51} \) \(\mathstrut -\mathstrut 3892q^{52} \) \(\mathstrut -\mathstrut 6662q^{53} \) \(\mathstrut -\mathstrut 320q^{55} \) \(\mathstrut +\mathstrut 3120q^{56} \) \(\mathstrut -\mathstrut 2160q^{57} \) \(\mathstrut -\mathstrut 960q^{58} \) \(\mathstrut +\mathstrut 840q^{60} \) \(\mathstrut +\mathstrut 3184q^{61} \) \(\mathstrut -\mathstrut 1144q^{62} \) \(\mathstrut +\mathstrut 468q^{63} \) \(\mathstrut +\mathstrut 9730q^{65} \) \(\mathstrut -\mathstrut 192q^{66} \) \(\mathstrut +\mathstrut 1748q^{67} \) \(\mathstrut -\mathstrut 28q^{68} \) \(\mathstrut -\mathstrut 1560q^{70} \) \(\mathstrut -\mathstrut 12136q^{71} \) \(\mathstrut -\mathstrut 540q^{72} \) \(\mathstrut -\mathstrut 1582q^{73} \) \(\mathstrut -\mathstrut 9300q^{75} \) \(\mathstrut +\mathstrut 5040q^{76} \) \(\mathstrut +\mathstrut 416q^{77} \) \(\mathstrut +\mathstrut 3336q^{78} \) \(\mathstrut -\mathstrut 6560q^{80} \) \(\mathstrut +\mathstrut 11502q^{81} \) \(\mathstrut +\mathstrut 3376q^{82} \) \(\mathstrut +\mathstrut 11308q^{83} \) \(\mathstrut -\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 5896q^{86} \) \(\mathstrut +\mathstrut 5760q^{87} \) \(\mathstrut +\mathstrut 480q^{88} \) \(\mathstrut +\mathstrut 630q^{90} \) \(\mathstrut -\mathstrut 14456q^{91} \) \(\mathstrut +\mathstrut 4648q^{92} \) \(\mathstrut -\mathstrut 6864q^{93} \) \(\mathstrut -\mathstrut 5400q^{95} \) \(\mathstrut -\mathstrut 15456q^{96} \) \(\mathstrut -\mathstrut 13102q^{97} \) \(\mathstrut -\mathstrut 2098q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
5.5.c.a \(2\) \(0.517\) \(\Q(\sqrt{-1}) \) None \(-2\) \(-12\) \(40\) \(-52\) \(q+(-1-i)q^{2}+(-6+6i)q^{3}-14iq^{4}+\cdots\)