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Properties

Label 197.3.c
Level $197$
Weight $3$
Character orbit 197.c
Rep. character $\chi_{197}(14,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $64$
Newform subspaces $1$
Sturm bound $49$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 197.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 197 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(49\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(197, [\chi])\).

Total New Old
Modular forms 68 68 0
Cusp forms 64 64 0
Eisenstein series 4 4 0

Trace form

\( 64 q - 2 q^{2} - 2 q^{3} - 10 q^{5} - 6 q^{8} + 10 q^{11} + 68 q^{12} + 2 q^{13} - 2 q^{14} - 280 q^{16} - 30 q^{17} - 68 q^{18} + 114 q^{20} - 20 q^{21} + 48 q^{23} + 60 q^{24} + 22 q^{27} + 392 q^{28}+ \cdots - 66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(197, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
197.3.c.a 197.c 197.c $64$ $5.368$ None 197.3.c.a \(-2\) \(-2\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{4}]$