Properties

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

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Defining parameters

Level: \( N \) \(=\) \( 7 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 7.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
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 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

Trace form

\( 6 q + 4 q^{2} - 3 q^{3} - 20 q^{4} + 165 q^{5} - 406 q^{7} - 1312 q^{8} + 42 q^{9} + 2580 q^{10} + 403 q^{11} + 5964 q^{12} - 5936 q^{14} - 20910 q^{15} + 3064 q^{16} + 8229 q^{17} + 6672 q^{18} + 29985 q^{19}+ \cdots + 1879428 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
7.7.d.a 7.d 7.d $2$ $1.610$ \(\Q(\sqrt{-3}) \) None 7.7.d.a \(12\) \(-21\) \(315\) \(-686\) $\mathrm{SU}(2)[C_{6}]$ \(q+12\zeta_{6}q^{2}+(-7-7\zeta_{6})q^{3}+(-80+\cdots)q^{4}+\cdots\)
7.7.d.b 7.d 7.d $4$ $1.610$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 7.7.d.b \(-8\) \(18\) \(-150\) \(280\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-4-4\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(6+3\beta _{1}+\cdots)q^{3}+\cdots\)