Properties

Label 7.3.b
Level 7
Weight 3
Character orbit b
Rep. character \(\chi_{7}(6,\cdot)\)
Character field \(\Q\)
Dimension 1
Newforms 1
Sturm bound 2
Trace bound 0

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Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(7, [\chi])\).

Total New Old
Modular forms 3 3 0
Cusp forms 1 1 0
Eisenstein series 2 2 0

Trace form

\(q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 5q^{4} \) \(\mathstrut -\mathstrut 7q^{7} \) \(\mathstrut -\mathstrut 3q^{8} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut +\mathstrut 21q^{14} \) \(\mathstrut -\mathstrut 11q^{16} \) \(\mathstrut -\mathstrut 27q^{18} \) \(\mathstrut +\mathstrut 18q^{22} \) \(\mathstrut +\mathstrut 18q^{23} \) \(\mathstrut +\mathstrut 25q^{25} \) \(\mathstrut -\mathstrut 35q^{28} \) \(\mathstrut -\mathstrut 54q^{29} \) \(\mathstrut +\mathstrut 45q^{32} \) \(\mathstrut +\mathstrut 45q^{36} \) \(\mathstrut -\mathstrut 38q^{37} \) \(\mathstrut +\mathstrut 58q^{43} \) \(\mathstrut -\mathstrut 30q^{44} \) \(\mathstrut -\mathstrut 54q^{46} \) \(\mathstrut +\mathstrut 49q^{49} \) \(\mathstrut -\mathstrut 75q^{50} \) \(\mathstrut -\mathstrut 6q^{53} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 162q^{58} \) \(\mathstrut -\mathstrut 63q^{63} \) \(\mathstrut -\mathstrut 91q^{64} \) \(\mathstrut -\mathstrut 118q^{67} \) \(\mathstrut +\mathstrut 114q^{71} \) \(\mathstrut -\mathstrut 27q^{72} \) \(\mathstrut +\mathstrut 114q^{74} \) \(\mathstrut +\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 94q^{79} \) \(\mathstrut +\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 174q^{86} \) \(\mathstrut +\mathstrut 18q^{88} \) \(\mathstrut +\mathstrut 90q^{92} \) \(\mathstrut -\mathstrut 147q^{98} \) \(\mathstrut -\mathstrut 54q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(7, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7.3.b.a \(1\) \(0.191\) \(\Q\) \(\Q(\sqrt{-7}) \) \(-3\) \(0\) \(0\) \(-7\) \(q-3q^{2}+5q^{4}-7q^{7}-3q^{8}+9q^{9}+\cdots\)