Properties

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

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 7.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q\)
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 3 3 0
Cusp forms 1 1 0
Eisenstein series 2 2 0

Trace form

\(q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut 15q^{4} \) \(\mathstrut +\mathstrut 49q^{7} \) \(\mathstrut -\mathstrut 31q^{8} \) \(\mathstrut +\mathstrut 81q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut 15q^{4} \) \(\mathstrut +\mathstrut 49q^{7} \) \(\mathstrut -\mathstrut 31q^{8} \) \(\mathstrut +\mathstrut 81q^{9} \) \(\mathstrut -\mathstrut 206q^{11} \) \(\mathstrut +\mathstrut 49q^{14} \) \(\mathstrut +\mathstrut 209q^{16} \) \(\mathstrut +\mathstrut 81q^{18} \) \(\mathstrut -\mathstrut 206q^{22} \) \(\mathstrut -\mathstrut 734q^{23} \) \(\mathstrut +\mathstrut 625q^{25} \) \(\mathstrut -\mathstrut 735q^{28} \) \(\mathstrut +\mathstrut 1234q^{29} \) \(\mathstrut +\mathstrut 705q^{32} \) \(\mathstrut -\mathstrut 1215q^{36} \) \(\mathstrut -\mathstrut 1294q^{37} \) \(\mathstrut -\mathstrut 334q^{43} \) \(\mathstrut +\mathstrut 3090q^{44} \) \(\mathstrut -\mathstrut 734q^{46} \) \(\mathstrut +\mathstrut 2401q^{49} \) \(\mathstrut +\mathstrut 625q^{50} \) \(\mathstrut -\mathstrut 5582q^{53} \) \(\mathstrut -\mathstrut 1519q^{56} \) \(\mathstrut +\mathstrut 1234q^{58} \) \(\mathstrut +\mathstrut 3969q^{63} \) \(\mathstrut -\mathstrut 2639q^{64} \) \(\mathstrut +\mathstrut 4946q^{67} \) \(\mathstrut +\mathstrut 2914q^{71} \) \(\mathstrut -\mathstrut 2511q^{72} \) \(\mathstrut -\mathstrut 1294q^{74} \) \(\mathstrut -\mathstrut 10094q^{77} \) \(\mathstrut -\mathstrut 3646q^{79} \) \(\mathstrut +\mathstrut 6561q^{81} \) \(\mathstrut -\mathstrut 334q^{86} \) \(\mathstrut +\mathstrut 6386q^{88} \) \(\mathstrut +\mathstrut 11010q^{92} \) \(\mathstrut +\mathstrut 2401q^{98} \) \(\mathstrut -\mathstrut 16686q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.b.a \(1\) \(0.724\) \(\Q\) \(\Q(\sqrt{-7}) \) \(1\) \(0\) \(0\) \(49\) \(q+q^{2}-15q^{4}+7^{2}q^{7}-31q^{8}+3^{4}q^{9}+\cdots\)