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Properties

Label 297.2.g
Level $297$
Weight $2$
Character orbit 297.g
Rep. character $\chi_{297}(98,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $20$
Newform subspaces $2$
Sturm bound $72$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 297 = 3^{3} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 297.g (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 99 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 2 \)
Sturm bound: \(72\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(297, [\chi])\).

Total New Old
Modular forms 84 28 56
Cusp forms 60 20 40
Eisenstein series 24 8 16

Trace form

\( 20 q - 10 q^{4} + 9 q^{5} + 12 q^{11} + 6 q^{14} - 10 q^{16} - 18 q^{20} + 6 q^{22} - 12 q^{23} - 3 q^{25} + q^{31} - 14 q^{37} - 66 q^{38} - 6 q^{47} - 4 q^{49} - 2 q^{55} + 120 q^{56} - 6 q^{58} - 9 q^{59}+ \cdots + 13 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(297, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
297.2.g.a 297.g 99.g $4$ $2.372$ \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) 99.2.g.a \(0\) \(0\) \(9\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(2-2\beta _{2})q^{4}+(2-\beta _{1}+\beta _{2})q^{5}+(\beta _{2}+\cdots)q^{11}+\cdots\)
297.2.g.b 297.g 99.g $16$ $2.372$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None 99.2.g.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{2}+\beta _{7}+\beta _{9}-\beta _{12}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(297, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(297, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(99, [\chi])\)\(^{\oplus 2}\)