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Properties

Label 7.5.b
Level $7$
Weight $5$
Character orbit 7.b
Rep. character $\chi_{7}(6,\cdot)$
Character field $\Q$
Dimension $1$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(7, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
7.5.b.a 7.b 7.b $1$ $0.724$ \(\Q\) \(\Q(\sqrt{-7}) \) \(1\) \(0\) \(0\) \(49\) $\mathrm{U}(1)[D_{2}]$ \(q+q^{2}-15q^{4}+7^{2}q^{7}-31q^{8}+3^{4}q^{9}+\cdots\)