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Properties

Label 49.3.f
Level $49$
Weight $3$
Character orbit 49.f
Rep. character $\chi_{49}(6,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $54$
Newform subspaces $1$
Sturm bound $14$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 49.f (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 49 \)
Character field: \(\Q(\zeta_{14})\)
Newform subspaces: \( 1 \)
Sturm bound: \(14\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(49, [\chi])\).

Total New Old
Modular forms 66 66 0
Cusp forms 54 54 0
Eisenstein series 12 12 0

Trace form

\( 54 q - 5 q^{2} - 7 q^{3} - 25 q^{4} - 7 q^{5} - 35 q^{6} - 3 q^{8} + 62 q^{9} - 7 q^{10} - 38 q^{11} - 42 q^{12} - 7 q^{13} + 77 q^{14} - 89 q^{15} - 21 q^{16} + 42 q^{17} + 12 q^{18} + 49 q^{20} - 7 q^{21}+ \cdots + 136 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(49, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
49.3.f.a 49.f 49.f $54$ $1.335$ None 49.3.f.a \(-5\) \(-7\) \(-7\) \(0\) $\mathrm{SU}(2)[C_{14}]$