↑

Properties

Label 196.3.o
Level $196$
Weight $3$
Character orbit 196.o
Rep. character $\chi_{196}(11,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $648$
Newform subspaces $1$
Sturm bound $84$
Trace bound $0$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 196.o (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 196 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 1 \)
Sturm bound: \(84\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(196, [\chi])\).

Total New Old
Modular forms 696 696 0
Cusp forms 648 648 0
Eisenstein series 48 48 0

Trace form

\( 648 q - 13 q^{2} - 13 q^{4} - 26 q^{5} - 2 q^{6} - 16 q^{8} - 176 q^{9} - 12 q^{10} + 45 q^{12} - 4 q^{13} + 89 q^{14} - 25 q^{16} - 26 q^{17} - 48 q^{18} - 166 q^{20} + 50 q^{21} + 10 q^{22} - 96 q^{24}+ \cdots + 771 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(196, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
196.3.o.a 196.o 196.o $648$ $5.341$ None 196.3.o.a \(-13\) \(0\) \(-26\) \(0\) $\mathrm{SU}(2)[C_{42}]$