Properties

Label 7.7.b
Level 7
Weight 7
Character orbit b
Rep. character \(\chi_{7}(6,\cdot)\)
Character field \(\Q\)
Dimension 3
Newforms 2
Sturm bound 4
Trace bound 1

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 7 \)
Character orbit: \([\chi]\) = 7.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q\)
Newforms: \( 2 \)
Sturm bound: \(4\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 5 5 0
Cusp forms 3 3 0
Eisenstein series 2 2 0

Trace form

\(3q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut +\mathstrut 17q^{4} \) \(\mathstrut -\mathstrut 77q^{7} \) \(\mathstrut +\mathstrut 601q^{8} \) \(\mathstrut -\mathstrut 1893q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(3q \) \(\mathstrut -\mathstrut 7q^{2} \) \(\mathstrut +\mathstrut 17q^{4} \) \(\mathstrut -\mathstrut 77q^{7} \) \(\mathstrut +\mathstrut 601q^{8} \) \(\mathstrut -\mathstrut 1893q^{9} \) \(\mathstrut +\mathstrut 3710q^{11} \) \(\mathstrut -\mathstrut 5215q^{14} \) \(\mathstrut +\mathstrut 4080q^{15} \) \(\mathstrut -\mathstrut 13087q^{16} \) \(\mathstrut +\mathstrut 27537q^{18} \) \(\mathstrut -\mathstrut 28560q^{21} \) \(\mathstrut +\mathstrut 3674q^{22} \) \(\mathstrut -\mathstrut 13258q^{23} \) \(\mathstrut +\mathstrut 42795q^{25} \) \(\mathstrut -\mathstrut 5831q^{28} \) \(\mathstrut +\mathstrut 1070q^{29} \) \(\mathstrut -\mathstrut 32640q^{30} \) \(\mathstrut -\mathstrut 16983q^{32} \) \(\mathstrut +\mathstrut 28560q^{35} \) \(\mathstrut +\mathstrut 12393q^{36} \) \(\mathstrut +\mathstrut 107198q^{37} \) \(\mathstrut -\mathstrut 199920q^{39} \) \(\mathstrut +\mathstrut 228480q^{42} \) \(\mathstrut -\mathstrut 63778q^{43} \) \(\mathstrut +\mathstrut 33354q^{44} \) \(\mathstrut -\mathstrut 280414q^{46} \) \(\mathstrut -\mathstrut 46893q^{49} \) \(\mathstrut -\mathstrut 76735q^{50} \) \(\mathstrut +\mathstrut 538560q^{51} \) \(\mathstrut -\mathstrut 102466q^{53} \) \(\mathstrut +\mathstrut 281281q^{56} \) \(\mathstrut -\mathstrut 281520q^{57} \) \(\mathstrut -\mathstrut 369334q^{58} \) \(\mathstrut -\mathstrut 598773q^{63} \) \(\mathstrut +\mathstrut 684721q^{64} \) \(\mathstrut +\mathstrut 199920q^{65} \) \(\mathstrut +\mathstrut 936558q^{67} \) \(\mathstrut -\mathstrut 228480q^{70} \) \(\mathstrut -\mathstrut 611290q^{71} \) \(\mathstrut -\mathstrut 1650831q^{72} \) \(\mathstrut +\mathstrut 862714q^{74} \) \(\mathstrut -\mathstrut 440482q^{77} \) \(\mathstrut +\mathstrut 1599360q^{78} \) \(\mathstrut -\mathstrut 140490q^{79} \) \(\mathstrut +\mathstrut 994563q^{81} \) \(\mathstrut -\mathstrut 538560q^{85} \) \(\mathstrut -\mathstrut 1642214q^{86} \) \(\mathstrut +\mathstrut 65050q^{88} \) \(\mathstrut -\mathstrut 1399440q^{91} \) \(\mathstrut -\mathstrut 386478q^{92} \) \(\mathstrut +\mathstrut 2480640q^{93} \) \(\mathstrut +\mathstrut 281520q^{95} \) \(\mathstrut +\mathstrut 2375177q^{98} \) \(\mathstrut -\mathstrut 861330q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7.7.b.a \(1\) \(1.610\) \(\Q\) \(\Q(\sqrt{-7}) \) \(9\) \(0\) \(0\) \(-343\) \(q+9q^{2}+17q^{4}-7^{3}q^{7}-423q^{8}+\cdots\)
7.7.b.b \(2\) \(1.610\) \(\Q(\sqrt{-510}) \) None \(-16\) \(0\) \(0\) \(266\) \(q-8q^{2}+\beta q^{3}-\beta q^{5}-8\beta q^{6}+(133+\cdots)q^{7}+\cdots\)