Properties

Label 7.5.d
Level 7
Weight 5
Character orbit d
Rep. character \(\chi_{7}(3,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 4
Newforms 1
Sturm bound 3
Trace bound 0

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 7.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
Sturm bound: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(7, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

Trace form

\(4q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 20q^{4} \) \(\mathstrut -\mathstrut 30q^{5} \) \(\mathstrut +\mathstrut 304q^{8} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 20q^{4} \) \(\mathstrut -\mathstrut 30q^{5} \) \(\mathstrut +\mathstrut 304q^{8} \) \(\mathstrut -\mathstrut 24q^{9} \) \(\mathstrut -\mathstrut 204q^{10} \) \(\mathstrut -\mathstrut 58q^{11} \) \(\mathstrut -\mathstrut 588q^{12} \) \(\mathstrut +\mathstrut 560q^{14} \) \(\mathstrut +\mathstrut 468q^{15} \) \(\mathstrut -\mathstrut 72q^{16} \) \(\mathstrut -\mathstrut 246q^{17} \) \(\mathstrut +\mathstrut 216q^{18} \) \(\mathstrut +\mathstrut 642q^{19} \) \(\mathstrut -\mathstrut 1050q^{21} \) \(\mathstrut -\mathstrut 1264q^{22} \) \(\mathstrut +\mathstrut 290q^{23} \) \(\mathstrut +\mathstrut 720q^{24} \) \(\mathstrut -\mathstrut 572q^{25} \) \(\mathstrut +\mathstrut 1008q^{26} \) \(\mathstrut -\mathstrut 28q^{28} \) \(\mathstrut -\mathstrut 2176q^{29} \) \(\mathstrut -\mathstrut 72q^{30} \) \(\mathstrut +\mathstrut 3618q^{31} \) \(\mathstrut +\mathstrut 1584q^{32} \) \(\mathstrut +\mathstrut 2070q^{33} \) \(\mathstrut -\mathstrut 2478q^{35} \) \(\mathstrut -\mathstrut 1632q^{36} \) \(\mathstrut -\mathstrut 270q^{37} \) \(\mathstrut -\mathstrut 6168q^{38} \) \(\mathstrut -\mathstrut 1428q^{39} \) \(\mathstrut -\mathstrut 1752q^{40} \) \(\mathstrut +\mathstrut 6048q^{42} \) \(\mathstrut +\mathstrut 2472q^{43} \) \(\mathstrut +\mathstrut 2412q^{44} \) \(\mathstrut +\mathstrut 1944q^{45} \) \(\mathstrut +\mathstrut 2384q^{46} \) \(\mathstrut -\mathstrut 1542q^{47} \) \(\mathstrut -\mathstrut 980q^{49} \) \(\mathstrut +\mathstrut 7568q^{50} \) \(\mathstrut -\mathstrut 4734q^{51} \) \(\mathstrut -\mathstrut 3192q^{52} \) \(\mathstrut -\mathstrut 4510q^{53} \) \(\mathstrut -\mathstrut 11016q^{54} \) \(\mathstrut -\mathstrut 1232q^{56} \) \(\mathstrut +\mathstrut 11052q^{57} \) \(\mathstrut -\mathstrut 904q^{58} \) \(\mathstrut +\mathstrut 2526q^{59} \) \(\mathstrut -\mathstrut 756q^{60} \) \(\mathstrut -\mathstrut 282q^{61} \) \(\mathstrut -\mathstrut 336q^{63} \) \(\mathstrut -\mathstrut 5472q^{64} \) \(\mathstrut +\mathstrut 5796q^{65} \) \(\mathstrut -\mathstrut 2556q^{66} \) \(\mathstrut -\mathstrut 1318q^{67} \) \(\mathstrut +\mathstrut 20412q^{68} \) \(\mathstrut +\mathstrut 3360q^{70} \) \(\mathstrut -\mathstrut 10408q^{71} \) \(\mathstrut -\mathstrut 1296q^{72} \) \(\mathstrut +\mathstrut 5214q^{73} \) \(\mathstrut +\mathstrut 4036q^{74} \) \(\mathstrut -\mathstrut 9636q^{75} \) \(\mathstrut -\mathstrut 8890q^{77} \) \(\mathstrut -\mathstrut 9072q^{78} \) \(\mathstrut -\mathstrut 8110q^{79} \) \(\mathstrut -\mathstrut 3144q^{80} \) \(\mathstrut +\mathstrut 9306q^{81} \) \(\mathstrut -\mathstrut 4032q^{82} \) \(\mathstrut +\mathstrut 588q^{84} \) \(\mathstrut -\mathstrut 15492q^{85} \) \(\mathstrut +\mathstrut 12928q^{86} \) \(\mathstrut +\mathstrut 5976q^{87} \) \(\mathstrut -\mathstrut 2912q^{88} \) \(\mathstrut +\mathstrut 33990q^{89} \) \(\mathstrut +\mathstrut 17640q^{91} \) \(\mathstrut -\mathstrut 20232q^{92} \) \(\mathstrut +\mathstrut 7446q^{93} \) \(\mathstrut +\mathstrut 27768q^{94} \) \(\mathstrut +\mathstrut 6558q^{95} \) \(\mathstrut -\mathstrut 37828q^{98} \) \(\mathstrut +\mathstrut 10368q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(7, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7.5.d.a \(4\) \(0.724\) \(\Q(\sqrt{-3}, \sqrt{22})\) None \(-4\) \(6\) \(-30\) \(0\) \(q+(-2+\beta _{1}-2\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)