↑

Properties

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

Related objects

Downloads

Learn more

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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(7, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
7.3.b.a 7.b 7.b $1$ $0.191$ \(\Q\) \(\Q(\sqrt{-7}) \) \(-3\) \(0\) \(0\) \(-7\) $\mathrm{U}(1)[D_{2}]$ \(q-3q^{2}+5q^{4}-7q^{7}-3q^{8}+9q^{9}+\cdots\)